For a given positive integer n, two integers a and b are called congruent modulo n,
written a == b (mod n) if, and only if n | (a - b)

Modulo is an equivalence relation - Reflexivity, Symmetry, Transitivity.

a = b + k n for some integer k
a and b have the same remainder when divided by n
For all integers a and n with n > 1, if gcd(a, n) = 1, 

then there exists an integer x such that as == 1 (mod n)
The integer s is called an inverse of a modulo n.