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Claim. Abderrahmane Nitaj, On a conjecture of Erdős on $3$-powerful numbers, Bull. London Math. Soc. 27 (1995), no. 4, 317--318, cited as [Ni95] on the problem page, proves Erdős's conjecture that $x+y=z$ has infinitely many solutions with $\gcd(x,y)=1$ in which every prime dividing $xyz$ divides it to at least the third power, that is, infinitely many triples of coprime $3$-powerful numbers $a,b,c$ with $a+b=c$; the paper constructs three explicit infinite families of such solutions. The statement is taken from the paper's summary in zbMATH (Zbl 0835.11013). This is the third question of Problem 939, answered yes.

Covers. The third question (infinitely many coprime $3$-powerful $a,b,c$ with $a+b=c$). 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: Bulletin of the London Mathematical Society, volume 27, issue 4, issued July 1995 (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 Nitaj with the answer to the third question 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.