{"schema":"vela.problem-packet.v0.1","problem":939,"statement":"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 $a+b=c$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}