Question 92
Let $p \ge 5$ be a prime number. Prove that for each divisor $d \gt 2$ of $p-1$ it's possible to partition all integers between $1$ and $p-1$ into the sets with $d$ numbers in each in such a way that the sum of squares of all numbers of each set is divisible by $p$.
(Mikhail Karpuk)
(Mikhail Karpuk)