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Modular Arithmetic

Let m in Z_>0 and define the selector function

x := such a in Z: x = [a]m.

+m: Zm x Zm -> Zm

x +m y := [x+Zy]m

-m: Zm -> Zm

-m x := [-Z x]m

*m: Zm x Zm -> Zm

x *m y := [x*Z y]m