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Equivalent Definition

+m: Zm x Zm -> Zm

[a]m +m [b]m : = [a+Zb]m

-m: Zm -> Zm

-m [a]m := [-Z a]m

*m: Zm x Zm -> Zm

[a]m *m [b]m : = [a*Z b]m

Because of congruence properties, functions are uniquely defined.