Show that can't be a power of 2 if ( ).
the claim would be true if we also assume that n > 1. the proof is quite easy: let it's clear that if is even, then is odd.
so we may assume that is odd. the proof now is by induction over we have suppose is a power of 2. then for
some and so which is never a power of 2 because if then the identity completes the proof.