[This is an attempt to rescue the deleted question https://math.stackexchange.com/questions/4230138/sum-of-a-list-of-squares]
Is there a set of $4042$ distinct positive integers that can be partitioned into two sets of $2021$ elements each with equal sums and equal sums of squares, that is, with
I can do it with three numbers on a side: $1^k+5^k+6^k=2^k+3^k+7^k$ for $k=1,2$,
and four numbers on a side: $1^k+4^k+6^k+7^k=2^k+3^k+5^k+8^k$ for $k=1,2$,
but $2021$ numbers on a side is a bit much for trial and error and/or hand calculation.
Is there an efficient, systematic way to produce these things?