Define equivalence relation on set of integers with 6 distinct equivalence classes

Question

I know an equivalence relation onto a set of integers, Z, is a relation that is reflexive, symmetric, and transitive. I also know that an equivalence class of "a" in "Z" is the set of elements "x" in "Z" such that (a,x) follow the relation. So I need exactly 6 different equivalence classes. I can't get my brain to just come up with a relation for any set of integers... Please help :)

Tl;dr - TITLE

Answer 1

A ~ B <=> A mod 6 = B mod 6 is probably the simplest example

Answer 2

For $n,m\in\mathbb Z$, define the equivalence relation $n\sim m$ if, and only if, the remainders of the division of n and m by 6 are equal.

Answer 3

Choose six integers, say $\{0,1,2,3,4,5\}$

Pick some relation such that none of these are in the same equivalence class, and that any other integer is in the same equivalence class as one of these.