MathNet 2006 — Part 03 Question 67

Suppose that the real numbers $a_{i} \in [-2,17]$, $i=1,2, \ldots, 59$, satisfy $a_{1}+a_{2}+\cdots+a_{59}=0$. Prove that
$$
a_{1}^{2}+a_{2}^{2}+\cdots+a_{59}^{2} \leq 2006 .
$$