CatalinBordea wrote: Let $ n $ be a positive integer and $ n $ real numbers $ a_1,a_2,\ldots ,a_n $ such that $ a_1^2+a_2^2+\cdots +a_n^2=1. $ Show that $$ \sum_{1\le ij\le n} a_ia_j<2\sqrt n. $$ Russian math competition It was here. Please use the search function.

How do you search these things? Also, ”Stars of Mathematics 2016” don't seem to work well, neither copy-pasting latex code.

CatalinBordea wrote: How do you search these things? Also, ”Stars of Mathematics 2016” don't seem to work well, neither copy-pasting latex code. Just search for "\sum_{1 \le ij \le n}" (after all it is this summation condition which makes the problem rather special).