The congruence modulo is an equivalence relation (also called a congruence relation), which defines a partition of the Gaussian integers into equivalence classes, called here congruence classes or residue classes. The set of the residue classes is usually denoted , or , or simply .
the congRueNce ModuLo is AN eQuIvALEncE rElAtIon (ALSo cAlleD a congRUence RelAtIoN), which deFiNeS a parTitIoN of ThE gAussian Integers intO equivaLEnCe clAssES, caLled heRE cOngrUence clAsseS OR ResidUe classeS. tHe seT oF THE Residue ClaSses IS uSuaLly dEnOted , or , or SImPLy .