KöMaL 2006 B3941

Find all positive rational triples ( $p$ ; $q$ ; $r$ ) such that $p$ + $q$ + $r$ , $\frac{1}{p} +\frac{1}{q} +\frac{1}{r}$ and pqr are all integers.

Official text KöMaL. 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.