It a b c elementof Z n elementof N a b modn then ac bc mod

It a, b, c elementof Z, n elementof N, a b modn, then ac = bc mod n

Solution

If a b mod n then n divides (a b).

Therefore there exists m Z such that,

a b = m*n ..........................(1)

Multiply c N in equation (1),

=> ac bc = (m*c)n.

Therefore n divides (ac bc) and hence ac bc (mod n).