Spring 2016, problem 13
Consider the binomial coefficients $\binom{n}{k}=\frac{n!}{k!(n-k)!}$, where $k\in\{1,2,\ldots, n-1\}$. Determine all positive integers $n$ for which $\binom{n}{1},\binom{n}{2},\ldots ,\binom{n}{n-1}$ are all even numbers.
Consider the binomial coefficients $\binom{n}{k}=\frac{n!}{k!(n-k)!}$, where $k\in\{1,2,\ldots, n-1\}$. Determine all positive integers $n$ for which $\binom{n}{1},\binom{n}{2},\ldots ,\binom{n}{n-1}$ are all even numbers.