Congruence Modulo \(n\) is an Equivalence Relation.

Given any integers \(a\text{,}\) \(b\text{,}\) and \(c\text{,}\) and any positive integer \(n\text{,}\) the following hold:

1. \(a \equiv a \pmod{n}\text{.}\)

2. If \(a \equiv b \pmod{n}\) then \(b \equiv a \pmod{n}\text{.}\)

3. If \(a \equiv b \pmod{n}\) and \(b \equiv c \pmod{n}\text{,}\) then \(a \equiv c \pmod{n}\text{.}\)

In other words, congruence modulo \(n\) is reflexive, symmetric, and transitive, so is an equivalence relation.