Question 143
Let $n$ be an odd number greater than 1, and let $f(x)$ be a polynomial of degree $n$ in $x$. It is known that $f(k) = 2^k$ for $k = 0, 1, \dots, n$. Prove that there are only finitely many integers $x$ for which the value of $f(x)$ is a power of 2.