Let $P$ be a polynomial with integer coefficients such that for every positive integer $n$, $P(n)$ divides $2^n - 1$.
Show that $P(x) =1$ or $P(x) = -1$ for all $x$.
Let $P$ be a polynomial with integer coefficients such that for every positive integer $n$, $P(n)$ divides $2^n - 1$.
Show that $P(x) =1$ or $P(x) = -1$ for all $x$.