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number > number theory > algebraic number theory > congruence

Preferred term

congruence

Definition(s)

Given an integer $n > 1$ , called a modulus, two integers $a$ and $b$ are said to be congruent modulo $n$ , if $n$ is a divisor of their difference: that is, if there is an integer $k$ such that:
${\\displaystyle a-b=kn.}$
Congruence modulo $n$ is a congruence relation, meaning that it is an equivalence relation that is compatible with the operations of addition, subtraction, and multiplication. Congruence modulo $n$ is denoted:
${\\displaystyle a\\equiv b{\\pmod {n}}.}$
The parentheses mean that $(mod n)$ applies to the entire equation, not just to the right-hand side (here, $b$ ).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Modular_arithmetic#Congruence)

Broader concept(s)

algebraic number theory

In other languages

congruence sur les entiers

French

URI

http://data.loterre.fr/ark:/67375/PSR-Q3G3SRHB-H

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