# Congruence relation

[https://en.wikipedia.org/wiki/Congruence\_relation](https://en.wikipedia.org/wiki/Congruence_relation)

In abstract algebra, a **congruence relation** is an equivalence relation on an algebraic structure (group, ring, etc.) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements.

Every congruence relation has a corresponding _quotient structure_, whose elements are the _equivalence classes_ (or _congruence classes_) for the relation.

The prototypical example of a congruence relation is congruence modulo `m` on `ℤ`, sometimes denoted `ℤ/mℤ`. For a given integer `m > 1`, two integers `a` and `b` are _congruent modulo `n`_, written `a ≡ b (mod n)`, if `a - b` is divisible by `m`, or, equivalently, if `a` and `b` have the same remainder `r` when divided by `m`.
