Modulus Operations Homework: Simplifying 1^3+2^3+3^3+...+99^3+100^3(mod4)

[Elruso]

Homework Statement

How do you simplify : 1^3+2^3+3^3+4^3+...+99^3+100^3(mod4)

Please try to explain the solution as detailed as possible or atleast so I can understand it.

 

[D H]

Use the fact that (4a+b)^3 mod 4 = b^3 mod 4. All you have to worry about are b=1,2,3,4. All of the other terms in the sum are duplicates.