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## Homework Statement

(a) Find the remainder when 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divided by 5.

(b) Generalize this result

## Homework Equations

Congruence Modulo

a[itex]\equiv[/itex]b mod n

also

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?

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