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- The '''integers''' ([[Latin]] word ''integer'' means "untouched") are the [[natural number]]s ([[1 (number)|1]], [[2 (nu ...d]] of [[rational number]]s, from other "integers" such as the [[algebraic integer]]s.10 KB (1,566 words) - 08:34, 2 March 2024
- 12 bytes (1 word) - 19:33, 3 November 2007
- 141 bytes (13 words) - 13:12, 13 June 2008
- 242 bytes (31 words) - 08:58, 8 December 2008
- 108 bytes (16 words) - 13:07, 14 June 2008
- * [http://www.research.att.com/~njas/sequences/ On-Line Encyclopedia of Integer Sequences] cf [[OEIS]]224 bytes (29 words) - 08:56, 8 December 2008
- Auto-populated based on [[Special:WhatLinksHere/Integer]]. Needs checking by a human.2 KB (247 words) - 17:28, 11 January 2010
Page text matches
- The product of an integer with another integer.84 bytes (11 words) - 10:06, 4 September 2009
- #REDIRECT[[integer]]20 bytes (2 words) - 21:02, 7 August 2007
- The smallest integer which is divided evenly by all given numbers.103 bytes (14 words) - 07:56, 29 June 2009
- ...'d''(''n'') or τ(''n'') or σ<sub>0</sub>(''n''), is the number of positive integer [[divisor]]s of the number ''n''. The value of ''d'' on a general integer ''n'' with prime factorisation720 bytes (123 words) - 04:26, 1 November 2013
- {{r|unit (algebraic integer)}} {{r|Gaussian integer}}887 bytes (126 words) - 02:29, 22 December 2008
- ...lic key]] encryption algorithm whose strength depends on the difficulty of integer factorisation.152 bytes (19 words) - 18:53, 29 July 2010
- ...'multiple''' of an [[integer]] is the product of that integer with another integer. For instance, 6 is a multiple of 2, since 6=2x3. Similarly, -6 is a mult924 bytes (151 words) - 22:50, 31 March 2008
- ...nent (group theory)|exponent]] of the [[multiplicative group]] modulo that integer. The value of λ on a general integer ''n'' with prime factorisation796 bytes (127 words) - 15:10, 2 December 2008
- Every positive integer can be expressed as a product of prime numbers in essentially only one way.134 bytes (20 words) - 15:55, 20 May 2008
- The number of additive partitions of a positive integer.92 bytes (12 words) - 16:28, 13 December 2008
- The exponent of the multiplicative group modulo an integer.95 bytes (12 words) - 17:59, 21 November 2008
- The number of integers less than or equal to and coprime to a given integer.112 bytes (18 words) - 17:47, 29 October 2008
- Holomorphic function characterized in that at integer values of its argument it can be interpreted as iterated exponent.156 bytes (21 words) - 14:27, 8 March 2009
- * [http://www.research.att.com/~njas/sequences/ On-Line Encyclopedia of Integer Sequences] cf [[OEIS]]224 bytes (29 words) - 08:56, 8 December 2008
- A function defined on the set of positive integers, usually with integer, real or complex values, studied in number theory.159 bytes (23 words) - 15:51, 2 December 2008
- ...uccessive positive integers raised to powers of a variable, typically with integer, real or complex coefficients.189 bytes (25 words) - 16:55, 4 December 2008
- A number which is the residue of a square integer with respect to a given modulus.118 bytes (19 words) - 02:28, 28 October 2008
- Probable prime (an integer which shares a property common to all prime numbers) which is not actually145 bytes (21 words) - 11:15, 4 September 2009
- A digital [[circuit]] that performs integer [[addition]] in the [[Arithmetic Logic Unit]] in a [[computer]].144 bytes (18 words) - 14:17, 8 December 2008
- ...mber which is not algebraic: that is, does not satisfy any polynomial with integer or rational coefficients.148 bytes (21 words) - 15:21, 31 October 2008
- The number of positive integer divisors of a given number.94 bytes (13 words) - 16:56, 6 December 2008
- ...tion an + bn = cn has no solutions in positive integers a, b, c if n is an integer greater than 2.156 bytes (26 words) - 07:18, 4 September 2009
- ...nction whose value is the sum of all positive divisors of a given positive integer.125 bytes (19 words) - 13:14, 5 December 2008
- A real number and is the integer between 1 and -1, which signifies a value of nothing.122 bytes (19 words) - 02:51, 3 June 2008
- ...maximize a real function by systematically choosing the values of real or integer variables from within an allowed set.206 bytes (31 words) - 10:34, 4 September 2009
- The assignment of data types (such as integer or string) to variables at the time of execution of a computer program, rat196 bytes (30 words) - 00:23, 2 October 2009
- ...uations and the theory of distributions, by generalising the concept of an integer index to a vector of indices.237 bytes (32 words) - 10:04, 4 September 2009
- ...f 27 data types with tag values starting with 1; for example, Boolean (1), integer (2), and bit string (3).224 bytes (27 words) - 03:37, 14 March 2024
- * [http://branchandcut.org/ COIN-OR SYMPHONY] - integer programming software, [[Common Public License]] *[[MINTO]] - integer programming solver using branch and bound algorithm. Freeware for personal2 KB (239 words) - 06:44, 20 March 2008
- ...rder''' of a [[group (mathematics)|group]] element is the least positive [[integer]] (if one exists) such that raising the element to that power gives the [[i The '''exponent''' of a group is the least positive [[integer]] (if one exists) such that raising any element of the group to that power857 bytes (146 words) - 13:24, 1 February 2009
- ...number]] ''p'' is a [[divisor]] of the [[multiplication|product]] of two [[integer]]s, ''ab'', then either ''p'' is a divisor of ''a'' or ''p'' is a divisor o ...and ''q'' are [[relatively prime]] integers and that ''p''|''kq'' for some integer ''k''. Then ''p''|''k''.2 KB (322 words) - 12:51, 18 December 2007
- For a group, its cardinality; for an element of a group, the least positive integer (if one exists) such that raising the element to that power gives the ident199 bytes (32 words) - 17:17, 20 November 2008
- ...ely prime in pairs and if b1, b2, …, bn are integers, then there exists an integer that is congruent to bi modulo mi for i=1,2, …, n.230 bytes (38 words) - 06:25, 4 September 2009
- An adder is a [[digital circuit]] designed to perform [[integer]] [[addition]] in the Arithmetic Logic Unit on board a computer. These circ *Where ''n'' is an integer from zero to (base - 1)2 KB (368 words) - 05:19, 17 March 2024
- ...tional relation between a part and the whole consisting of a numerator (an integer — the part) and a denominator (a natural number — the whole).217 bytes (33 words) - 08:31, 2 June 2008
- .../math> and <math>x</math> and <math>y</math> represent the smallest such [[integer|integers]] (i.e., they are [[mutually prime]]). ...; therefore <math>x</math> must also be even. This means that there is an integer <math>k</math> such that <math>x = 2 \times k</math>. Inserting it back int2 KB (307 words) - 04:13, 14 October 2010
- ...ometry]] a '''divisor''' on an [[algebraic variety]] is a formal sum (with integer coefficients) of [[subvariety|subvarieties]]. An '''effective divisor''' is a sum with non-negative integer coefficients.818 bytes (138 words) - 10:54, 18 February 2009
- ...ion with parameter ''n'' assigns probability proportional to 1/''r'' to an integer ''r'' ≤ ''n'' and zero otherwise, with [[normalization]] factor ''H''<su ...nd ''s'' assigns probability proportional to 1/''r''<sup>''s''</sup> to an integer ''r'' ≤ ''n'' and zero otherwise, with normalization factor <math>\sum_{1 KB (168 words) - 16:41, 6 February 2009
- ...roper divisor''. The number 0 is not considered to be a divisor of ''any'' integer. :5 divides 0 because <math>5 \cdot 0 = 0</math>. In fact, every integer except zero divides zero.4 KB (594 words) - 02:37, 16 May 2009
- In [[number theory]] the '''sum-of-divisors function''' of a positive integer, denoted σ(''n''), is the sum of all the positive [[divisor]]s of the numb The value of σ on a general integer ''n'' with prime factorisation1 KB (172 words) - 04:53, 1 November 2013
- ...ted with, all logarithms notably absent. If <math>z = n</math>, a positive integer, all but finitely many terms in the series cancel and we are left with ...ction as <math>\Gamma'(z) = \Gamma(z) \psi(z)</math>; the derivative at an integer is then <math>\Gamma'(n) = (H_{n-1} - \gamma)(n-1)!</math> and in particula3 KB (488 words) - 10:34, 13 November 2007
- ...th>+</math> (addition), the unary function <math>-</math> (which maps each integer to its [[inverse]]), and the binary relation <math><</math>. This structure ...<math>f\colon \mathbb Z\rightarrow\mathbb Z</math> which multiplies every integer by 2 is a homomorphism from the structure <math>(\mathbb Z, 0, +, -, <)</ma2 KB (348 words) - 16:37, 10 March 2009
- ...]. The ''n''-th cyclotomic polynomial, denoted by Φ<sub>''n''</sub> has [[integer]] cofficients. For a positive integer ''n'', let ζ be a primitive ''n''-th root of unity: then1 KB (206 words) - 14:55, 11 December 2008
- ...is a function defined on the set of [[positive integer]]s, usually with [[integer]], [[real number|real]] or [[complex number|complex]] values.1 KB (159 words) - 06:03, 15 June 2009
- Given any positive integer ''n'' we can define functions ''f'' and ''F'' as follows: ...mial function each of whose coefficients is 1/n<nowiki>!</nowiki> times an integer. It satisfies the identity2 KB (325 words) - 06:31, 15 September 2009
- {{r|integer factorisation}}259 bytes (33 words) - 18:53, 29 July 2010
- ...n the [[multiplicative group]] taken [[modular arithmetic|modulo]] a given integer. Let ''N'' be a positive integer and write ('''Z'''/''N'')* for the multiplicative group of integers modulo2 KB (335 words) - 06:03, 15 June 2009
- {{r|Integer factorization}}307 bytes (40 words) - 11:59, 15 June 2009
- ...ber: ''a + 0 = 0 + a = a''. For any integer ''a'', ''(a + 1)'' means least integer greater than ''a'', also known as successor of ''a''.1 KB (163 words) - 02:33, 30 October 2008
- {{r|integer}}207 bytes (26 words) - 19:20, 23 June 2009
- {{r|Integer}}119 bytes (13 words) - 20:13, 11 September 2009
- In the program, we create an instance of the class integer. ...cally, the traditional class relationship is held in the class diagram. An integer is a Real. A Real(float) is a (subset of) complex. An a complex number is a9 KB (1,125 words) - 07:07, 8 August 2009
- ...partition of a set or an ordered partition of a set, or a partition of an integer, or a partition of an interval.198 bytes (34 words) - 10:41, 4 September 2009
- {{r|Gaussian integer}}276 bytes (34 words) - 10:41, 21 April 2010
- {{r|Integer}}203 bytes (25 words) - 18:31, 26 October 2008
- ...s thus [[group isomorphism|isomorphic]] to the [[additive group]] of the [[integer]]s, or to an additive group with respect to a fixed [[modular arithmetic|mo362 bytes (57 words) - 20:28, 31 January 2009
- In many languages, the 5 literal will represent an integer. It will be automatically cast into a string '5' and appended to the prior ...would be equal to the integer it is being compared with. Similarly, if the integer had been converted into a string, it would be equal to the string it is bei3 KB (514 words) - 08:02, 20 March 2024
- Any efficient solution to the [[integer factorisation]] problem would break RSA; see the [[RSA algorithm#RSA_and_fa ...to speed up the sieving step in the [[number field sieve]] technique for [[integer factorisation]].1 KB (215 words) - 05:48, 8 April 2024
- {{r|Integer}}225 bytes (28 words) - 13:16, 14 June 2008
- ...range of [[holomorphism]] of function, but out of holomorphism of some its integer [[iterate]]552 bytes (81 words) - 00:43, 10 July 2013
- {{r|Integer}}454 bytes (55 words) - 03:14, 21 October 2010
- ...m{SL}_2(\mathbf{Z}))</math>, consisting of 2 by 2 [[matrix|matrices]] with integer entries and [[determinant]] 1, is referred to as the modular group. An [[gr1 KB (235 words) - 19:47, 15 December 2010
- Any [[subring]] of an [[algebraic number field]] composed of [[algebraic integer]]s forms an order: the ring of all algebraic integers in such a field is th307 bytes (47 words) - 13:58, 1 February 2009
- {{r|Integer}}350 bytes (42 words) - 12:01, 12 June 2009
- * The map defined on the ring of [[integer]]s which maps an integer to its remainder modulo ''N'' for some fixed modulus ''N'' is a ring homomo2 KB (283 words) - 10:23, 6 January 2011
- the integer types of arguments, integer, float, imaginary, complex and matrix.3 KB (332 words) - 07:07, 8 August 2009
- ...ime factor then μ(''n'') is defined to be zero. If ''n'' is [[square-free integer|square-free]], then μ(''n'') = +1 if ''n'' has an even number of prime fac2 KB (261 words) - 04:58, 10 December 2008
- Mathematical function <math>A</math> of two variables, such that for integer arguments <math>n,n</math> it can be expressed as follows:362 bytes (58 words) - 05:15, 2 February 2009
- {{r|Integer}}430 bytes (55 words) - 15:47, 11 January 2010
- {{r|Integer}}449 bytes (60 words) - 20:34, 11 January 2010
- {{r|Integer}}429 bytes (55 words) - 21:08, 11 January 2010
- {{r|integer}}224 bytes (27 words) - 11:52, 29 November 2008
- invokes different operation if A, B, and C are integer, floating point, or string variables.784 bytes (106 words) - 10:25, 7 February 2009
- The '''integers''' ([[Latin]] word ''integer'' means "untouched") are the [[natural number]]s ([[1 (number)|1]], [[2 (nu ...d]] of [[rational number]]s, from other "integers" such as the [[algebraic integer]]s.10 KB (1,566 words) - 08:34, 2 March 2024
- ...ne whose [[leading coefficient]] is 1, then ''x'' is called an [[algebraic integer]]. ...t{2}</math> is an algebraic number of degree 2, and, in fact, an algebraic integer. It is not rational, so must have degree greater than 1. As it is a root o7 KB (1,145 words) - 00:49, 20 October 2013
- {{r|Integer}}495 bytes (63 words) - 18:42, 11 January 2010
- {{r|Integer}}494 bytes (62 words) - 20:40, 11 January 2010
- {{r|Integer}}515 bytes (63 words) - 21:04, 11 January 2010
- {{r|Integer}}515 bytes (67 words) - 16:26, 11 January 2010
- {{r|Integer}}480 bytes (62 words) - 16:24, 11 January 2010
- {{r|Integer}}522 bytes (67 words) - 20:03, 11 January 2010
- ...n as the '''fundamental theorem of arithmetic''' states that every nonzero integer can be written in a unique way as a product of a [[unit (multiplicative)|un ...rsion as follows. The first part of the theorem states that every nonzero integer ''n'' has a prime factorization. We can therefore write9 KB (1,496 words) - 06:25, 23 April 2008
- {{r|Integer}}606 bytes (79 words) - 20:34, 11 January 2010
- {{r|Integer}}626 bytes (79 words) - 16:01, 11 January 2010
- {{r|Integer}}594 bytes (76 words) - 19:15, 11 January 2010
- ...function''' ''p''(''n'') counts the number of [[partition]]s of a positive integer ''n'', that is, the number of ways of expressing ''n'' as a sum of positive483 bytes (70 words) - 16:32, 13 December 2008
- {{r|Integer}}618 bytes (80 words) - 16:24, 11 January 2010
- {{r|Integer}}633 bytes (79 words) - 19:23, 11 January 2010
- {{r|Integer}}675 bytes (89 words) - 17:28, 11 January 2010
- ...' of an [[integer]] ''n'' is an expression of ''n'' as a sum of [[positive integer]]s ("parts"), with the order of the terms in the sum being disregarded.2 KB (336 words) - 07:17, 16 January 2009
- int number; // integer variable, it only accepts integers number = "7"; // "7" is a string, not the integer value 7, error5 KB (772 words) - 07:11, 8 August 2009
- ...cubic reciprocity is most naturally expressed in terms of the [[Eisenstein integer]]s, that is, the ring ''E'' of [[complex number]]s of the form where and ''a'' and ''b'' are [[integer]]s and2 KB (319 words) - 15:45, 27 October 2008
- {{r|Integer}}858 bytes (112 words) - 15:35, 11 January 2010
- ...ssive [[positive integer]]s raised to powers of a variable, typically with integer, real or complex coefficients. If the series converges, its value determin2 KB (398 words) - 11:44, 15 June 2009
- ...g by a square integer, we may assume that ''d'' is in fact a [[square-free integer]]. As above, we take ''d'' to be a square-free integer. The [[maximal order]] of ''F'' is3 KB (453 words) - 17:18, 6 February 2009
- ...les of commutative operations are [[addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In695 bytes (102 words) - 19:40, 31 January 2009
- ...o a [[triangle]]. Every simplex has a dimension, which is a nonnegative [[integer]]; an n-simplex means a simplex of dimension n.749 bytes (127 words) - 17:13, 14 November 2007
- {{r|Integer}}969 bytes (124 words) - 18:42, 11 January 2010
- ...conjecture is the [[odd Goldbach conjecture]]: this states that every odd integer greater than 5 can be expressed as a sum of three odd primes. Goldbach's co ...d integers. In particular, this implies that every sufficiently large even integer can be expressed as a sum of four primes. The work did not give an explicit2 KB (340 words) - 23:24, 14 February 2010
- ...an be expanded. It is the identity that states that for any non-negative [[integer]] ''n'', ...p;+ ''y'')<sup>''n''</sup> as an infinite series when ''n'' is not an integer or is not positive.3 KB (507 words) - 07:34, 9 August 2010
- ...the whole complex plane (it has [[countable set]] of poles at the negative integer values of the argument), but [[logarithm]] is not, because it has cutline a839 bytes (128 words) - 10:05, 10 October 2013
- The integer ''n'' defined by the theorem is the '''Weierstrass degree''' of ''f''.745 bytes (116 words) - 13:35, 8 March 2009
- Length 8-bit unsigned integer. The length of the option1 KB (182 words) - 22:53, 12 April 2011
- ...is a number that can be expressed as a [[ratio]] of two [[integer]]s. Non-integer rational numbers (commonly called [[fraction]]s) are usually written as the ...the rational numbers as an [[equivalence class]] of [[ordered pair]] of [[integer]]s <math>\left(a, b\right)</math>, with <math>b</math> not equal to zero.9 KB (1,446 words) - 08:52, 30 May 2009
- {{r|Integer}}1 KB (146 words) - 16:32, 11 January 2010
- ...ic]], i.e. it is not a root of any [[polynomial]] whose coefficients are [[integer]]s, or, equivalently, it is not a root of any polynomial whose coefficients875 bytes (130 words) - 12:27, 8 May 2008
- is defined as the least integer ''n'' such that whenever the [[complete graph]] <math> K_n</math>&nbs968 bytes (163 words) - 05:01, 1 November 2013
- ...Any integer equals one of these modulo 13. That is, the remainder when any integer is divided by 13 must be one of these. ...to the discrete log problem modulo an integer would imply a solution for [[integer factorisation]], so it would also break the [[RSA cryptosystem]] which is b5 KB (772 words) - 17:15, 6 August 2013
- '''0''' ('''zero''') is a [[real number]] and is the [[integer]] between [[1 (number)|1]] and [[-1 (number)|-1]], which signifies a value1 KB (232 words) - 03:30, 6 November 2009
- {{r|Integer}}1 KB (169 words) - 19:54, 11 January 2010
- ...e absolute conductor of an abelian number field ''F'' is then the smallest integer ''f'' such that ''F'' is a [[subfield]] of the field of ''f''-th roots of u1 KB (177 words) - 01:07, 18 February 2009
- Integer constants are written as numbers, optionally prefixed with a base and the o Erlang also provides another syntactic shortcut: you can write an integer as the dollar sign (<code>$</code>) and a character, and the value is the A4 KB (623 words) - 07:07, 8 August 2009
- {{r|Integer}}1 KB (180 words) - 17:00, 11 January 2010
- {{r|Integer}}1 KB (174 words) - 20:03, 11 January 2010
- The Baer-Specker group is the group ''B'' = '''Z'''<sup>'''N'''</sup> of all integer sequences with componentwise addition, that is, the [[direct product]] of [1 KB (151 words) - 16:18, 4 January 2013
- ...it primes, can be encrypted to themselves." Key size is also variable; any integer number of bits. For AES use, the block size would be fixed at 128 bits and1 KB (179 words) - 05:49, 8 April 2024
- A function ''f'' has a pole of order ''k'', where ''k'' is a positive integer, at a point ''a'' if the limit1 KB (188 words) - 13:32, 8 March 2009
- For instance, suppose we start with an empty stack of [[integer]]s, and then push the object 5. The stack now contains one object, and the Has-a Integer SP, initially 03 KB (537 words) - 00:36, 9 February 2010
- ...e''' is a technique for estimating the size of "sifted sets" of [[positive integer]]s which satisfy a set of conditions which are expressed by [[Congruence re * Almost all integer polynomials (taken in order of height) are irreducible.3 KB (494 words) - 15:55, 29 October 2008
- {{r|Integer}}2 KB (206 words) - 19:38, 11 January 2010
- ...h> where ''r'' and ''s'' are integers [[coprime]] to ''p'' and ''n'' is an integer. We define the ''p''-adic valuation <math>| \cdot |_p</math> on '''Q''' by1 KB (168 words) - 12:39, 4 January 2009
- ...e and SampleFormat tags, which specify the size and type (signed/unsigned, integer/floating-point) of pixels stored in the image.1 KB (189 words) - 04:27, 7 October 2013
- {{r|Integer}}2 KB (229 words) - 09:18, 6 March 2024
- Roots of unity are clearly [[algebraic number]]s, and indeed [[algebraic integer]]s. It is often convenient to identify the ''n''-th roots of unity with th1 KB (197 words) - 22:01, 7 February 2009
- where n is an integer greater than or equal to 1. In acid-base reaction n is the number of proton1 KB (199 words) - 11:08, 1 September 2009
- ...f <math>K = \mathbf{Q}(\sqrt d)</math> with <math>d</math> a [[square-free integer]] then <math>O_K = \mathbf{Z}[a]</math> where <math>a = (1+\sqrt d)/2</math1 KB (208 words) - 16:47, 17 December 2008
- ...l axis; for non-negative integer values of the argument, this function has integer values. For integer <math>n</math>, the <math>n!</math> gives the number of ways in which ''n''22 KB (3,358 words) - 09:31, 10 October 2013
- ...ory]], '''Jordan's totient function''' <math>J_k(n)</math> of a [[positive integer]] ''n'', named after [[Camille Jordan]], is defined to be the number of ''k1 KB (181 words) - 16:05, 29 October 2008
- where <math>a_0\,</math> is some integer and all the other numbers <math>a_k\,</math> are positive integers. Let <ma2 KB (252 words) - 11:44, 2 December 2010
- ...]]s associated to [[quadratic form]]s. They are [[modular form]]s of half-integer [[weight of a modular form|weight]].1 KB (161 words) - 04:13, 3 January 2009
- Many common number systems, such as the [[integer]]s, the [[rational number]]s, the [[real number]]s, and the [[complex numbe2 KB (240 words) - 10:48, 21 September 2013
- Let X be a stochastic variable taking non-negative integer values with [[probability density function]]2 KB (233 words) - 09:15, 14 September 2013
- ...sfer function <math>f</math> is called also [[logistic operator]]. The non-integer iterates of <math>f</math> can be expressed through the logistic sequence a The non-integer iterations of the logistic operator can be constructed using the analytic c9 KB (1,388 words) - 11:08, 20 November 2011
- ...boson]]s, particles of integer spin and he showed that photons have indeed integer spin ''S'' = 1. The spin multiplicity 2''S''+1 = 3 is given by two componen4 KB (577 words) - 13:21, 3 November 2021
- Auto-populated based on [[Special:WhatLinksHere/Integer]]. Needs checking by a human.2 KB (247 words) - 17:28, 11 January 2010
- ...riptstyle c\ </math> divides <math>\scriptstyle a^c - a\ </math> for every integer <math>\scriptstyle a\ </math>. A Carmichael number ''c'' also satisfies the *Every Carmichael number is [[square-free integer|square-free]] and has at least three different prime factors4 KB (576 words) - 12:00, 1 January 2013
- ...e details of the difference between a rational number and a fraction (with integer numerator and denominator)—this will not cause any problems; ful ...ns <math>\frac{a}{c}</math> and <math>\frac{b}{d},</math> with integer numerators and natural denominators, are called '''neighbors''' (in the giv35 KB (5,836 words) - 08:40, 15 March 2021
- ...on process, or the oscillator that generates the carrier wave, may produce integer multiples, called harmonics, of any or all of these signals.2 KB (270 words) - 12:56, 22 September 2020
- ...showed that the functions ''g'' are [[polynomial]] functions of ''p'' with integer coefficients: these are the ''Hall polynomials''.2 KB (264 words) - 22:53, 19 February 2010
- ...]], the '''totient function''' or '''Euler's φ function''' of a [[positive integer]] ''n'', denoted φ(''n''), is defined to be the number of positive inte1 KB (224 words) - 17:35, 21 November 2008
- ...n some realizations, there may be some problems while one of arguments are integer and another is complex. In some programming languages, including [[Mathemat In some cases of integer <math>a</math> the function has specific names.8 KB (1,339 words) - 13:11, 8 August 2021
- ...nce if for any real number <math>\epsilon>0</math> there exists a positive integer <math>N(\epsilon)</math>, dependent on <math>\epsilon</math>, such that <ma1 KB (240 words) - 12:30, 4 January 2009
- {{r|Integer}}2 KB (277 words) - 16:52, 11 January 2010
- Define the ''radical'' of an integer to be the product of its distinct prime factors2 KB (301 words) - 13:18, 13 January 2013
- where ''n'' is an integer.2 KB (253 words) - 18:00, 10 February 2010
- primes :: [Integer]2 KB (254 words) - 06:06, 28 December 2009
- ...urn out to be groups. These include familiar number systems, such as the [[integer]]s, the [[rational number]]s, the [[real number]]s, and the [[complex numbe A group that we are introduced to in elementary school is the [[integer]]s under [[addition]].19 KB (3,074 words) - 11:11, 13 February 2009
- ==An Example with Integer Solutions==8 KB (1,339 words) - 11:08, 15 September 2009
- ...Fermat pseudoprime to base <math>\scriptstyle b\cdot q+a</math> for every integer <math>\scriptstyle b \ge 0</math>.2 KB (267 words) - 07:56, 15 June 2009
- ...d in stringed musical instruments, all vibration frequencies are typically integer multiples of the fundamental frequency. In more complex systems, such as th2 KB (288 words) - 13:04, 19 February 2022
- ** The usual [[order (relation)|order]] on the [[integer]]s is transitive: if ''x''>''y'' and ''y''>''z'' then ''x''>''z'';2 KB (295 words) - 14:28, 6 February 2009
- ...can be expressed as the residue of ''a''<sup>2</sup> modulo ''N'' for some integer ''a''. A '''quadratic non-residue''' of ''N'' is a number which is not a q2 KB (341 words) - 02:20, 28 October 2008
- This is valid for ''every'' integer ''k'' > 0, as the values of the zeta function at nonpositive integers are a ...g to each object again is a quotient whose denominator involves a rational integer defined in terms of the object raised to the ''-s'' power.7 KB (1,113 words) - 10:50, 4 October 2013
- ''zero'' is an integer, a rational number (the fraction 0/1),2 KB (326 words) - 18:28, 17 July 2009
- [[Integer arithmetic]] requires much less [[silicon real estate]] to implement than c3 KB (378 words) - 12:03, 6 March 2024
- ...les of associative operations are [[addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In2 KB (295 words) - 14:56, 12 December 2008
- #For any positive integer ''n'', if <math>A_1,A_2,\ldots,A_n \in \mathcal{A}</math> then <math>A_1 \c2 KB (324 words) - 16:34, 27 November 2008
- ...elation between a part and the whole. It consists of a [[numerator]] (an [[integer]] — the part) and a [[denominator]] (a [[natural number]] — the whole). ...we cannot compute an [[#Equivalent fractions|equivalent fraction]] with an integer numerator and a natural number denominator. A fraction with equal numerator21 KB (3,089 words) - 10:08, 28 February 2024
- ** The ring of [[integer]]s '''Z'''2 KB (326 words) - 09:55, 23 December 2008
- [[Integer arithmetic]] requires much less [[silicon real estate]] to implement than c2 KB (319 words) - 00:29, 28 November 2008
- (namely, ''x'' = −1) if ''x'' is supposed to be an [[integer|integer number]].6 KB (951 words) - 05:01, 8 December 2009
- ...allest common multiple''' of several [[integer]]s is the smallest positive integer that is a [[multiple (mathematics)|multiple]] of each of them. In [[algebr6 KB (743 words) - 18:42, 2 July 2009
- ...pressed with integer constant. Attempts to call [[Nest]] to evaluate a non–integer iterate of a function are interpreted as error. ==Non–integer iterate==15 KB (2,340 words) - 08:27, 9 September 2020
- The fraction on the right side is in lowest terms, and therefore there is an integer <math>c</math> so that2 KB (397 words) - 12:24, 14 May 2008
- ...has the form <math>6n - 1\ </math> or <math>6n + 1\ </math> (with ''n'' an integer), but there are also composite numbers of this form: 25, 35, 49, 55, 65, 772 KB (296 words) - 23:58, 20 February 2010
- * Let ''M'' be the [[positive integer]]s with multiplication as the operation. The corresponding convolution is2 KB (338 words) - 17:41, 23 December 2008
- ...r ''s'' assigns probability proportional to 1/''n''<sup>''s''</sup> to the integer ''n'': the normalizing factor is then the value of the [[Riemann zeta funct3 KB (389 words) - 13:28, 2 January 2009
- <math>k</math> is also integer number, <math>0\le k < N</math>. ...algorithms allow the efficient evaluation even if <math>N</math> is not an integer power of 2, although for the fast evaluation <math>N</math> should not have9 KB (1,368 words) - 11:59, 8 September 2020
- An example structure for a linked list of integer values in [[C programming language|C]] would be:2 KB (422 words) - 16:03, 30 July 2009
- * Discovery of an efficient solution to the [[integer factorisation]] problem would break RSA. See [[#RSA and factoring | below]] Given an efficient solution to the [[integer factorisation]] problem, breaking RSA would become trivial. The attacker is7 KB (1,171 words) - 05:48, 8 April 2024
- * The free group on a single element ''g'' is the additive group of [[integer]]s with <math>n \leftrightarrow g^n</math>.2 KB (436 words) - 02:56, 15 November 2008
- ...ower]] <math>n \geq 3</math>, it is impossible to find a trio of nonzero [[integer]]s <math>x, y, \text{ and } z</math> satisfying the equation2 KB (340 words) - 12:36, 22 February 2012
- ...of a group. A motivating example of a semigroup is the set of positive [[integer]]s with [[multiplication]] as the operation.3 KB (405 words) - 16:21, 13 November 2008
- <math>m_1+m_2+m_3=0</math>, <math>j_1+j_2 + j_3</math> is integer, <math>|m_i| \le j_i</math> and <math>|j_1-j_2|\le j_3 \le j_1+j_2</math>.3 KB (444 words) - 13:59, 31 December 2022
- * <code>INTEGER</code>, <code>REAL</code>, <code>DOUBLE PRECISION</code>, <code>COMPLEX</co3 KB (481 words) - 04:23, 4 August 2009
- ...t is equal to the binomial coefficient for the partition of ''n'' into two integer numbers. However, the two coefficients (binomial and multinomial) are nota2 KB (365 words) - 06:50, 22 January 2009
- For non-integer values of <math>c</math>, the iterated exponential can be defined as At non-integer values of <math>c</math>, <math>L</math> and <math>L^*</math> are [[branch6 KB (1,021 words) - 12:18, 11 June 2009
- ...1} \stackrel{f_i}{\rightarrow} G_i</math>, indexed by some subset of the [[integer]]s. A sequence will be termed ''exact at the term'' <math>G_i</math> if th3 KB (471 words) - 17:22, 15 November 2008
- ...e main exception to this is the most common case, where a polynomial has [[integer]] coefficients but one desires real number solutions. If, instead, one dem3 KB (418 words) - 14:53, 4 March 2009
- ...oblem of [[integer factorisation]], determining the factors of a composite integer, is famously difficult. Some factors may be easy — for example, 2 is ...an <math>m</math>. The related decision problem of determining whether an integer is prime or composite was recently shown to be in P. <ref>M. Agrawal, N. Ka15 KB (2,548 words) - 21:03, 20 August 2010
- # The [[integer]]s (<math> \scriptstyle \mathbb{Z} </math>) also include negative numbers, # A complex number that is solution to a [[polynomial]] in integer coefficients is an [[algebraic number]]. This set includes all rational num11 KB (1,701 words) - 20:07, 1 July 2021
- ...n [[algorithm]] for finding the [[greatest common divisor]] (gcd) of two [[integer]]s. The algorithm does not require [[prime number|prime factorizations]] a Thus the largest integer that is a divisor of ''both'' 1989 and 867 is 51. One use of this fact is7 KB (962 words) - 12:05, 3 May 2016
- ...viewing the [[prime number]]s as building blocks from which [[positive]] [[integer]]s can be assembled.3 KB (464 words) - 19:45, 1 December 2008
- ...sequence corresponding to ''t''=''n'' as ''n'' runs through the [[positive integer]]s is mapped to a non-convergent Cauchy sequence on the circle.3 KB (441 words) - 12:23, 4 January 2009
- * On the [[integer]]s, [[parity]]: <math>m \equiv n</math> iff ''m'',''n'' have the same [[rem3 KB (477 words) - 17:43, 14 October 2009
- ...e''' is a technique for estimating the size of "sifted sets" of [[positive integer]]s which satisfy a set of conditions which are expressed by [[Congruence re3 KB (473 words) - 15:39, 9 December 2008
- 7. The underlying type of an enum shall be a built-in CLS integer type (see clause 8.5.2). System.FlagsAttribute custom attribute. One represents named integer values, the other named10 KB (1,525 words) - 15:51, 23 December 2007
- ...work in number theory significantly impacted the field. His insights into integer partitions, where numbers are expressed as sums of smaller positive integer3 KB (352 words) - 14:08, 23 August 2023
- ...ose of a group. A motivating example of a monoid is the set of positive [[integer]]s with [[multiplication]] as the operation.3 KB (526 words) - 11:02, 23 December 2008
- In the integers, every integer ''n'' has four trivial divisors: 1, -1, ''n'', -''n''.3 KB (515 words) - 21:49, 22 July 2009
- If <math>n</math> is a positive integer, the symmetric group on <math>n</math> "letters" (often denoted <math>S_{n} .../math> are in [[one-to-one correspondence]] with the [[partition]]s of the integer n. Two permutations in <math>S_{n}</math> are [[conjugate]] in <math>S_{n}<8 KB (1,392 words) - 20:52, 25 June 2009
- ...al noise''') to emphasise that the exponent of the spectrum could take non-integer values and be closely related to [[fractional Brownian motion]], but the te3 KB (541 words) - 19:57, 18 September 2021
- {{r|Integer}}3 KB (441 words) - 12:55, 13 November 2014
- ...e bound into colourless, multiple quark states which have charges that are integer multiples of ''e'' and only at high energies, such as top quark decay, do t3 KB (454 words) - 09:43, 30 March 2011
- The series converges in the whole complex $z$ plane, but fails at negative integer values of <math>\alpha</math> . The postfix form of [[factorial]] is used a3 KB (459 words) - 07:58, 13 July 2012
- ...a structures with [[random access]] to all its elements using an [[integer|integer number]] as index. It is typically implemented as a continuous range in mem7 KB (1,246 words) - 17:24, 31 July 2008
- ...''K''</sub>. This may be seen as the [[integral closure]] of the ring of [[integer]]s '''Z''' in ''K''. The ring of integers is an [[order]], this is, a ring7 KB (1,077 words) - 17:18, 10 January 2009
- ...'S'' to be a finite set of prime numbers and define an ''S''-unit to be an integer divisible only by the primes in ''S''.3 KB (381 words) - 16:02, 28 October 2008
- ''Example 1.'' "A randomly chosen positive integer is even with probability 0.5." a positive integer chosen at random must have more than one decimal digit, since18 KB (2,797 words) - 14:37, 30 January 2011
- ...f</math> from the set <math>X=\{(x,y)\}</math> of all ''pairs'' (x,y) of [[integer|positive integers]] to the set of all positive integers given by formula <m4 KB (618 words) - 22:24, 7 February 2010
- Such definition is valid only for positive integer <math>z</math>. and extend the range of validity to the integer values larger than <math>-2</math>.21 KB (3,134 words) - 09:12, 10 October 2013
- ...r from 999999 to 000000). Because the end bit indicating positive/negative integer may flip over, some systems may revert the date to 20:45:52, Friday, Decemb9 KB (1,386 words) - 09:02, 2 March 2024
- ...M</math> array of integers, row major, with <math>S_{int}</math> bytes per integer. Given the array's base address <math>B</math>, to select the element from3 KB (572 words) - 07:34, 26 September 2007
- ...tion''. These operations are defined so as to emulate and generalize the [[integer]]s. Other common examples of rings include the ring of [[polynomial]]s of o ...er of elements is <math>\mathbb{Z}_5</math>, the set of remainders when an integer is divided by 5, i.e. the set {0,1,2,3,4} with operations such as 4 + 4 = 310 KB (1,667 words) - 13:47, 5 June 2011
- ...d as a [[fraction]] ''m'' / ''n'' in which ''m'' and ''n'' are [[integer]]s.4 KB (666 words) - 11:23, 3 October 2009
- ...sub>, …, ''y''<sub>''n''</sub> (where ''n'' is a arbitrary positive integer). Furthermore, the inequality is in fact an equality4 KB (629 words) - 16:46, 17 December 2008
- ...the rule: all variables with names beginning with I, J, K, L, M, and N are integer, the variables of which the names start with the other letters are real. ...ters, which gave rise to names as "CNVRG" for "convergence", "ITHR" for an integer threshold, etc. Moreover, the Fortran standard, up to and including Fortran20 KB (3,045 words) - 23:17, 6 October 2013
- ...<math>n=1, 2, 3</math> (theoretically, <math>n</math> can be any positive integer, but since <math>n</math> stands for the dimension of the space in which th4 KB (604 words) - 23:44, 30 November 2010
- ...degree'' of a non-zero sequence (''a''<sub>''n''</sub>) as the the largest integer ''d'' such that4 KB (604 words) - 23:54, 20 February 2010
- The [[integer]]s together with addition is a cyclic group. Consider the required properti ...ator''. Whenever ''a'' and ''b'' are integers, <math>a+b</math> is also an integer, and so the operation is closed on the group.15 KB (2,535 words) - 20:29, 14 February 2010
- ...that the coefficient of ''H''<sub>''n''</sub>(''x'') is equal to the even integer 2''n'',4 KB (580 words) - 06:31, 31 May 2009
- :<math>F_n\ </math> is the nearest integer to <math>\frac{1}{\sqrt{5}}\cdot \left(\frac{1+\sqrt{5}}{2}\right)^n<5 KB (743 words) - 13:10, 27 July 2008
- ...ction, where the result for any input string is always a fixed-size, large integer. An example of a hash digest is [[Hash_(cryptography)#SHA-1|SHA-1]], whic4 KB (586 words) - 15:45, 8 April 2024
- ...number''' is a number that can be evenly divided by exactly two positive [[integer|whole numbers]], namely 1 and itself. The first few prime numbers are 2, 3, A prime number is usually defined as a positive [[integer]] other than 1 that is (evenly) [[divisor|divisible]] only by 1 and itself.14 KB (2,281 words) - 12:20, 13 September 2013
- ...example, the problem [[integer factorization|''FACTORIZE'']] is: given an integer written in [[binary number|binary]], return all of the [[prime number|prime ...' otherwise, while the problem ''IS-COMPOSITE'' determines whether a given integer is ''not'' a prime number (i.e. a [[composite number]]). When ''IS-PRIME''17 KB (2,637 words) - 13:14, 6 November 2010
- ...with eigenvalues proportional to 1/''n''², where ''n'' is a positive integer, referred to as [[principal quantum number]]. Observe the somewhat unexpect ...has eigenvalues proportional to ''ℓ(ℓ+1)'', where ''ℓ'' is a non-negative integer (the [[azimuthal quantum number]], also known as the [[angular momentum qua19 KB (2,981 words) - 18:31, 3 November 2021
- A '''prime number''' is a [[integer|whole number]] greater than 1 that can be evenly divided by only two differ ...e numbers that can be written as <math> 2^{2^n}+1</math> for some positive integer ''n''. Such prime numbers make a surprising appearance in the solution to18 KB (2,917 words) - 10:27, 30 August 2014
- ...using the corresponding rules for binary addition and multiplication. Non-integer quantities can be represented as binary digits to the right of the binary p8 KB (1,318 words) - 08:17, 25 September 2007
- ...e, 4 is an integer, but its multiplicative inverse is 1/4, which is not an integer.18 KB (2,669 words) - 08:38, 17 April 2024
- where ''N'' is an unknown integer, <math>A_0,A_1,\ldots,A_N \in \mathbb{R}</math> and <math>\phi_1,\phi_2,\l4 KB (713 words) - 01:42, 10 February 2010
- Thick lines correspond to the Integer values.5 KB (731 words) - 10:07, 2 December 2013
- ...anged according to its mass m(M) and its mass excess/defect ∆m(M) = m(M) - integer[m(M)]. When expressing the mass m in daltons, (in metrology terms: [m] = Da * round(''m'') and ''A''·Ke are the '''integer masses''' of the molecule in kendricks.10 KB (1,572 words) - 15:08, 16 November 2010
- as an integer linear combination of the numbers (''a'',''b'') = ''ra'' + ''sb'' (with in5 KB (797 words) - 04:57, 21 April 2010
- Let <math>y_n=\left(\frac{1}{2}+n\right)d~</math> for integer values <math>n</math>, and <br>6 KB (884 words) - 18:03, 8 September 2020
- ...We can define the set of processes <math>\mathcal{L}(X)</math> that we can integer with respect to <math>X</math> :5 KB (858 words) - 12:47, 29 December 2008
- ...positive numbers are to its right and negative numbers to its left. The [[integer]]s (positive or negative "whole numbers") ..., −3, −2 ...owed that neither [[logarithm|e]] nor <math>e^2</math> can be a root of an integer [[quadratic equation]], and then established existence of transcendental nu19 KB (2,948 words) - 10:07, 28 February 2024
- ...a C<sub>2</sub>H<sub>2</sub> (sometimes written as HCCH), but the simplest integer ratio of elements is CH, which is the empirical formula of the acetylene mo11 KB (1,558 words) - 21:27, 10 November 2020
- ...rs as value elements. Our hash function would, given a string, produce an integer. We would then store or retrieve a reference to that person's phone number5 KB (832 words) - 13:00, 16 January 2008
- ...it vector is back at an angle between 0° and 360°. Therefore, for positive integer ''k'', ...one arrives again at a position between 0° and 360°, so that for positive integer ''k'',19 KB (3,106 words) - 09:53, 10 October 2013
- ...the [[Schrödinger equation]] for [[hydrogen-like atom]]s. It is a positive integer (''n'' = 1, 2, 3, …) that indexes [[atomic shell]]s. Historically,5 KB (873 words) - 15:11, 15 May 2022
- ...extensions are possible, in this article ''ℓ'' and ''m'' are restricted to integer numbers. For even ''m'' the associated Legendre function is a polynomial,7 KB (1,150 words) - 07:58, 24 January 2010
- Observe that if ''k'' is any integer, then the function: where ''m'' and ''n'' are non-zero [[integer]]s, ''A<sub>mn</sub>'' is an arbitrary constant and:15 KB (2,332 words) - 04:52, 18 October 2009
- ...overflow]] flag in a flags register may also be set (see the discussion of integer range below). ===Integer range===37 KB (5,596 words) - 21:55, 26 April 2008
- (where <math>d</math> is any positive integer), we can find a complex number <math>t</math> so that5 KB (924 words) - 16:35, 11 December 2008
- ...4 and multiply them together, you get another number - in fact, you get an integer. You don't get an apple or a pair of scissors or a bicycle. When computers ...ible that foo() could have used a decimal number (a 'float') as well as an integer. This potentially requires the programmer to write two or more near-identic25 KB (3,897 words) - 01:49, 8 October 2013
- and so on. Most of larger numbers have no single-character mames; the integer numbers are denoted using the [[positional numeral system]].6 KB (916 words) - 15:07, 16 July 2011
- ...the domain of [[factorial]]s to non-integers. The factorial of a positive integer ''n'', written ''n''!, is the product 1·2·3···''n''. The gamma functio ...png|thumb|250px|It is easy to graphically interpolate the factorial to non-integer values, but is there a formula that describes the resulting curve?]]32 KB (5,024 words) - 12:05, 22 December 2008
- or infinitely many rational points on a given curve (or surface)? What about integer points? ''x'' and ''y'' are both rational. This is the same as asking for all integer solutions27 KB (4,383 words) - 08:05, 11 October 2011
- where mathematically <math>n</math> can be any [[integer]]. where we have labelled the energy by the integer <math>n</math>.16 KB (2,810 words) - 11:31, 5 April 2011
- The second argument is unsigned integer, that indicates value <math>N=2^q</math>; where <math>q</math> is assumed t8 KB (1,204 words) - 18:09, 8 September 2020
- ...out that the quotient of two such lengths is given by a simple ratio of [[integer]]s. ...l waves. This can also create periodic waves if the single frequencies are integer multiples of each other or differently said if the overtones of the same fu11 KB (1,798 words) - 03:46, 13 September 2013
- ...{\beta}=im</math>, or <math>\beta=-m^2</math>, where <math>m</math> is any integer.8 KB (1,340 words) - 07:25, 27 October 2007
- ...oups are precisely the modules over <math>\mathbb{Z}</math>, the ring of [[integer]]s. If <math>G</math> is an Abelian group (written additively), one define7 KB (1,154 words) - 02:39, 16 May 2009
- ...''=±1 and spin an odd multiple of 1/2, and ''[[meson]]s'' with ''B''=0 and integer spin. The hadrons are classified further according to their ''[[strong isos6 KB (907 words) - 07:58, 28 May 2022
- ...ng of the automatic procedure for calculation of [[superfuncion]]s and non-integer iterates of holomorphic functions. Up to year 2014, such an automatic proce8 KB (1,169 words) - 01:26, 9 September 2014
- ...action is found [[experiment]]ally, and, for most basic reactions, is an [[integer]] value.7 KB (1,127 words) - 05:54, 31 October 2011
- * E = {x | x is a positive integer} ...s in the British Library" or "E is the set of all x, where x is a positive integer".22 KB (3,815 words) - 15:46, 23 September 2013
- ...been extended to allow many other types of exponents, including [[negative integer]]s, [[rational number]]s, [[real number]]s, [[complex number]]s, and even [8 KB (1,297 words) - 14:49, 12 December 2008
- ...tation of huge numbers in the [[mathematics of computation]]. For positive integer values of its argument <math>x</math>, tetration <math>\mathrm{tet}_b(x)</m ...onential function|exponential]] <math>\exp^c(z)</math> for the case of non-integer values of the number <math>c</math> of iterations.65 KB (10,203 words) - 04:16, 8 September 2014
- *integer - 36 KB (903 words) - 15:28, 24 August 2009