1. The problem statement, all variables and given/known data. show that if n devides a^n-b^n then n devides the quotient (a^n-b^n)/(a-b). here n,a,b are natural numbers with a and b distinct. 2. Relevant equations. 3. The attempt at a solution. i know i have to assume that n divides a^n-b^n. So, then a^n-b^n when divided by n will yield a remainder of 0. Therefore, one can say that a^n-b^n is congruent to o in (mod n). So a^n-b^n=0(mod n) then, a^n=b^n(mod n). but then i am stuck... i don't know if i am approaching it from the right direction. If am, am still very stuck. thanks for any help.