SOLUTION: For what integral values of n is the expression 1^n + 2^n + 3^n + 4^n divisible by 5? I'd really appreciate any offered help. Thanks.

Question 26823: For what integral values of n is the expression 1^n + 2^n + 3^n + 4^n divisible by 5?
I'd really appreciate any offered help. Thanks.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
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 ...
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