Question 32
Find all positive integers $n$ for which there exists an integer $m$ such that
$$
\frac{1}{n} \sum_{k=m}^{m+n-1} k^2
$$
is a perfect square. For example, when $n=7$ one can take $m=-3$.
$$
\frac{1}{n} \sum_{k=m}^{m+n-1} k^2
$$
is a perfect square. For example, when $n=7$ one can take $m=-3$.