Prove that if a is a natural number, then there exists two unequal natural numbers k and l for which $$ a^k - a^l $$ is divisible by 10.
I'm strangely lost on this one. I understand the pigeonhole principle but I'm unsure how to apply it here. Any help is greatly aprpeciated.
HINT: Consider the possible last digits of powers of $a$. There are at most how many different possibilities?