# Math Help - Congruence

1. ## Congruence

Prove that for any integer a, a^4 ≡ 0 or 1 (mod 5)

2. Hello,
Originally Posted by terencet
Prove that for any integer a, a^4 ≡ 0 or 1 (mod 5)
Test this out

If $a \equiv 0 (\bmod 5)$ then $a^4 \equiv ?? (\bmod 5)$ ?
If $a \equiv 1 (\bmod 5)$ then $a^4 \equiv ?? (\bmod 5)$ ?
If $a \equiv 2 (\bmod 5)$ then $a^4 \equiv ?? (\bmod 5)$ ?
If $a \equiv 3 (\bmod 5)$ then $a^4 \equiv ?? (\bmod 5)$ ?
If $a \equiv 4 (\bmod 5)$ then $a^4 \equiv ?? (\bmod 5)$ ?

Otherwise, you can use Fermat's little theorem, which says : for p prime, if a is not a multiple of p, then $a^{p-1} \equiv 1 (\bmod p)$