I'm working through the problems in Niven's number theory book, and problem 46 in section 1.2 (page 19) has me stumped.
Prove that there are no positive integers $a, b, n > 1$ such that $(a^n - b^n) | (a^n + b^n)$.
I've tried playing around a bit (e.g. noticing that $a^n - b^n$ must divide $2a^n$ and $2b^n$), but in general I've just been going around in circles. Can anyone please provide a (small) hint in the right direction?