Question 26823
For what integral values of n is the expression 1^n + 2^n + 3^n + 4^n divisible by 5?
WE CAN EASILY SEE THAT FOR N=1,2,3 ETC..IT IS DIVISIBLE BY 5..FOR EX...FOR N=1,WE HAVE 
1^1+2^1+3^1+4^1=1+2+3+4=10 WHICH IS DIVISIBLE BY 5..SIMILARLY FOR N=2,3 ETC..
IF YOU WANT A PROOF OF THE THEOREM USE INDUCTION METHOD ...