Made up number theory problem

Prove that, for all positive integers x and r, the remainder when is divided by is 1.

This is pretty easy if you interpret it as:



Which, according to the binomial theorem, is:



If we expand this out, then every term except for the first will be divisble by (x-1). The first term is just 1, so the remainder is 1. Nifty, right? I thought so.