Question 42
(CZS) Let $a_1,a_2,\ldots,a_n$ $(n\ge2)$ be a sequence of integers. Show that there is a subsequence $a_{k_1},a_{k_2},\ldots,a_{k_m}$, where $1\le k_1\lt k_2\lt\cdots\lt k_m\le n$, such that $a_{k_1}^2+a_{k_2}^2+\cdots+a_{k_m}^2$ is divisible by $n$.