Let x be any positive integer greater than 1 , which is not divisible by 17.

Prove that either x^8-1, or x^8+1, is divisible by 17.

(In reply to More generally (spoiler) by Steve Herman)

Well anticipated! In fact, if (2^n-2)/n is an integer, say x, then n (n>1) is prime, and x is A064535 in Sloane.

Posted by broll on 2011-09-06 02:32:31