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Direct Approach

Definition: Let m in Z_>0 and Z_m := {x in Z: 0 <= x < m}.

+m: Z x Z -> Zm

x +m y := (x + y) mod m

-m: Z x Z -> Zm

-m x := (-x) mod m

*m: Z x Z -> Zm

x *m y := (x * y) mod m