(a) Find the remainder when 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divided by 5.
(b) Generalize this result
a[itex]\equiv[/itex]b mod n
a=n*q+b where q is some integer.
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?