Question 45
Prove that there exists a sequence of positive integers $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ such that
$$
a_{1}^{2}+a_{2}^{2}+\cdots+a_{n}^{2}
$$
is a perfect square for every positive integer $n$.
$$
a_{1}^{2}+a_{2}^{2}+\cdots+a_{n}^{2}
$$
is a perfect square for every positive integer $n$.