Question 41
Find all sequences $a_{0} \leqslant a_{1} \leqslant a_{2} \leqslant \ldots$ of real numbers such that
$$
a_{m^{2}+n^{2}}=a_{m}^{2}+a_{n}^{2}
$$
for all integers $m, n \geqslant 0$.
$$
a_{m^{2}+n^{2}}=a_{m}^{2}+a_{n}^{2}
$$
for all integers $m, n \geqslant 0$.