Equivalence relation and Equivalence classes?

I'm not sure on the following question:

(a) Define a relation R on **Z** by

if and only if

Show that R is an equivalence relation, and describe the equivalence classes.

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I'm particularly interested on how you prove the transativity part of the equivalence relation and how to describe the equivalence classes. Can anyone help?

(also any more explanation on Equivalence relations and classes would be much appreciated as I could certainly do with understanding it better.)