Originally Posted by

**cassiopeia1289** Ok, so I did the problem and got a solution that another classmate didn't get. Now its got me paranoid, I don't know whose right.

"What is the remainder when the following sum is divided by 4?": $\displaystyle 1^5 + 2^5 + 3^5 + ... + 99^5 + 100^5$

So I'll briefly explain - I did:

so that is $\displaystyle \equiv 25(1^5 + 2^5 + 3^5 + 0^5)$ (mod 4)

worked it all out so that it is now congruent to 1(1 + 0 + 0) (mod 4)

Thus, the remainder is 1, yes??

My classmate go that there was no remainder. Did I do something wrong in calculations??