congruence class

In our entry on congruences we note that if m is not zero and a, b and c are any integers, then we have the following:

These three properties are just what we need to show that the integers are divided into exactly m congruence classes containing integers mutually congruent modulo m. (Technically, we say congruence is an equivalence relation.) For example, modulo five we have the 5 classes

Modulo two there are the two classes we call the even and odd integers:

Sometimes we denote these classes as 0 mod 2, and 1 mod 2 respectively.

See Also: Residue

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