What is an equivalence modulo?

Answer 1

An equivalence relationship is a relationship over the set of integers defined for as follows:

For equivalence modulo n (n being a positive integer),

a ~ b (mod n) <=> n divides (a-b)

This partitions the set of integers into n equivalence classes: {0, 1, 2, ... , n-1}.

Answer 2

An equivalence modulo is a relation between elements of a set, where two elements are considered equivalent if they have the same remainder when divided by a fixed number called the modulus. For example, in modulo 5 arithmetic, the equivalence class of 2 would include all numbers that leave a remainder of 2 when divided by 5: {2, 7, 12, 17, ...}. Equivalence modulo is often used in number theory and modular arithmetic.