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...e structure but using a' = a+b, b' = a-b) does not have that property when modular arithmetic is involved, but the PHT variant does.

...h satisfy a set of conditions which are expressed by [[Congruence relation#Modular arithmetic|congruence]]s. It was developed by [[Atle Selberg]] in the 1940s.

...ples are Z₂, the set {0,1} under addition and multiplication [[modular arithmetic|modulo]] 2. Other examples are Z₃ and Z₅, ... , Z<su

In [[modular arithmetic]], a '''quadratic residue''' for the [[modulus]] ''N'' is a number which ca

...h satisfy a set of conditions which are expressed by [[Congruence relation#Modular arithmetic|congruence]]s. It was developed by [[Pál Turán]] in 1934.

...aracter (group theory)|character]] on the [[multiplicative group]] taken [[modular arithmetic|modulo]] a given integer.

...results connecting the solvability of two related [[cubic equation]]s in [[modular arithmetic]]. It is a generalisation of the concept of [[quadratic reciprocity]].

The '''Chinese remainder theorem''' is a mathematical result about [[modular arithmetic]]. It describes the solutions to a system of [[linear congruence]]s with d

...ed to avoid loss or corruption of data, involve coefficients governed by [[modular arithmetic|arithmetic modulo 2]]. Polynomials with complex number coefficients or coe

...th>\scriptstyle a\ </math>. A Carmichael number ''c'' also satisfies the [[modular arithmetic|congruence]] <math>\scriptstyle a^{c-1} \equiv 1 \pmod c</math>, if <math>\

...of CH₂ groups they contain. When measuring their masses with [[modular arithmetic]] using the mass m(CH₂) as the modulus, all homologous molecules Math has a tool called [[modular arithmetic]] that can reveal the same homologous relation using the [[modulo operation

...derlying problems, most public-key algorithms involve operations such as [[modular arithmetic|modular]] multiplication and exponentiation, which are much more computatio

...te groups]] such as the [[cyclic group]]s that are the group of integers [[modular arithmetic|modulo]] ''n''. [[Set theory]] is a branch of [[logic]] and not technically

For example, let <math>R</math> be the ring of integers [[modular arithmetic|modulo 15]],

...[[random number]]s, which were added to the plaintext using the rules of [[modular arithmetic]]; each page was used only once, after which it was destroyed. Computer imp

Mathematics is not [[numerology]]. Numerology uses [[modular arithmetic]] to reduce names and dates down to numbers, but assigns emotions or traits