SE-SKOLORNAS 1974 Problem 6

For which $n$ can we find positive integers $a_1,a_2,\dots,a_n$ such that $a_1^2+a_2^2+\cdots+a_n^2$ is a square?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.