Problem 939

Erdős Problem #939: declared status 'open'. Formalized: yes. Let $r\geq 2$. An $r$-powerful number $n$ is one such that if $p\mid n$ then $p^r\mid n$. If $r\geq 4$ then can the sum of $r-2$ coprime $r$-powerful numbers ever be itself $r$-powerful? Are there at most finitely many such solutions? Are there infinitely many triples of coprime $3$-powerful numbers $a,b,c$ such that $a+b=c$? Prize: no. Tags: number theory.