MathNet 2015-part-05 — 191 problems (EN–VI) Question 96

For each positive integer $n$, define $s(n) = \sum_{k=0}^{n} r_{k}$, where $r_{k}$ is the remainder when $\binom{n}{k}$ is divided by $3$. Find all positive integers $n$ such that $s(n) \geq n$.