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.