what is the remainder when the following sum is divided by 4

what is the remainder when the following sum is divided by 4?
1^5+2^5+3^5+...+99^5+100^5
This problem is for a number theory class.

Solution

Note that the first four terms (1,32,243,1024) give remainders (when divided by 4) 1,0,-1 and 0 respectively and the remainders repeat in the same fashion.

Sum of the remainders in each set is 0.(there are 25 such sets as the sum is from 1 to 100).

So the required remainder is 0