ILL 1974 Problem 20

For which natural numbers $n$ do there exist $n$ natural numbers $a_i\ (1\le i\le n)$ such that $\sum_{i=1}^n a_i^{-2}=1$ ?

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.