1. The problem statement, all variables and given/known data (a) Find the remainder when 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divided by 5. (b) Generalize this result 2. Relevant equations Congruence Modulo a[itex]\equiv[/itex]b mod n also a=n*q+b where q is some integer. 3. The attempt at a solution The remainder for 1^99 would be 1. The remainder for 5^99 would be 0. I'm having difficulty finding the remainder for 2,3,4. I'm assuming I have to use modular arithmetic to find the remainder for these, but I'm not sure where to start. Anyone care to point me in the right direction?