Question 13
Let $(a_n)_{n \ge 1}$ be an arithmetic sequence of positive integers and let $S_n = a_1^2 + a_2^2 + \dots + a_n^2$, $n \in \mathbb{N}^*$. Prove that:
a) if $p \ge 5$ is a prime number, then $p$ divides $S_p$;
b) $S_5$ is not a square.
a) if $p \ge 5$ is a prime number, then $p$ divides $S_p$;
b) $S_5$ is not a square.