For each positive integer $n$, define $s(n) =\sum_{k=0}^n r_k$, where $r_k$ is the remainder when $n \choose k$ is divided by $3$. Find all positive integers $n$ such that $s(n) \ge n$. Malik Talbi
Problem
Source: 2015 Saudi Arabia GMO TST II p4
Tags: Binomial, remainder, number theory, combinatorics, inequalities