Congruence Modulo Proof

1. The problem statement, all variables and given/known data

Suppose n is an integer which is not a divisor of 5.

Prove that ##n^{4} \equiv 1 mod5##



3. The attempt at a solution

I know that 16 mod 5 is equivalent to 1 mod5.



##16 = 2^{4}##



2 is not a divisor of 5. How do I prove this for the general case?



I know

##n^{4} -1 = 5k, ## for some k ##\in Z##