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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 exponent of the multiplicative group modulo an integer.95 bytes (12 words) - 17:59, 21 November 2008
- The number of additive partitions of a positive integer.92 bytes (12 words) - 16:28, 13 December 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
- ...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
- A digital [[circuit]] that performs integer [[addition]] in the [[Arithmetic Logic Unit]] in a [[computer]].144 bytes (18 words) - 14:17, 8 December 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}}494 bytes (62 words) - 20:40, 11 January 2010
- {{r|Integer}}495 bytes (63 words) - 18:42, 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