MathNet 1998 — Part 01 Question 65

Let $n$ be a positive integer. Count the number of numbers $k \in \{0,1,2, \ldots, n\}$ such that $\binom{n}{k}$ is odd. Show that this number is a power of two, i.e. of the form $2^{p}$ for some nonnegative integer $p$.