Problem

Source: Mathematical Danube Competition 2016, Juniors P1

Tags: romania, algebra



Let $S=x_1x_2+x_3x_4+\cdots+x_{2015}x_{2016},$ where $x_1,x_2,\ldots,x_{2016}\in\{\sqrt{3}-\sqrt{2},\sqrt{3}+\sqrt{2}\}.$ Can $S$ be equal to $2016?$ Cristian Lazăr