Modular Arithmetic in Z:

Definition: a(modm) stands for the remainder when a is divided by m.

Definition: a(modm) + b(modm) is (a+b)(modm).

Definition: a(modm)xb(modm) is axb(modm).

Definition: a≡b(modm): a and b leave same remainder when divided by m

Theorem: If a≡b(modm) and c≡d(modm) then a+b≡c+d(modm)

Example: 3mod4 + 2mod4 ≡ 5mod4 ≡ 1mod4