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Claim. J. H. E. Cohn, A conjecture of Erdős on $3$-powerful numbers, Math. Comp. 67 (1998), no. 221, 439--440, cited as [Co98] on the problem page, proves that $x+y=z$ has infinitely many solutions in pairwise coprime $3$-powerful positive integers $x$, $y$, $z$ none of which is a perfect cube, a further conjecture that Nitaj's 1995 construction left unverified. The statement is taken from the paper's summary in zbMATH (Zbl 0957.11043). It answers the third question of Problem 939 yes, independently of Nitaj's claim.

Covers. The third question (infinitely many coprime $3$-powerful $a,b,c$ with $a+b=c$), with the added property that none of $a$, $b$, $c$ is a cube. Not covered: the first two questions, about sums of $r-2$ coprime $r$-powerful numbers for $r\geq4$.

Depends on. No page of this wiki; the proof is the paper's own.

Acceptance. Refereed: Mathematics of Computation, volume 67, issue 221, January 1998 (the Crossref record; the issue carries no publication day, so this page is named by the first day of its month). The site's curator, Thomas F. Bloom, credits Cohn's construction in the problem page's remarks, where the label is OPEN; commentary on a problem the site labels open is not acceptance, so the credit is recorded and not listed as reviewed.