Problem

Source: 2015 Saudi Arabia IMO TST II p3

Tags: inequalities, algebra, n-variable inequality



Let $a_1, a_2, ...,a_n$ be positive real numbers such that $$a_1 + a_2 + ... + a_n = a_1^2 + a_2^2 + ... + a_n^2$$Prove that $$\sum_{1\le i<j\le n} a_ia_j(1 - a_ia_j) \ge 0$$Võ Quốc Bá Cẩn.