Nitaj (1995): On a conjecture of Erdős on 3-powerful numbers

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Abderrahmane Nitaj, On a conjecture of Erdős on 3-powerful numbers, Bulletin of the London Mathematical Society 27 (1995), no. 4, 317--318, doi:10.1112/blms/27.4.317 (publisher Wiley; issued July 1995; bibliographic data from Crossref). The article is paywalled and no copy is held (no purchase), so no folder-name PDF exists and its theorem numbering and proof have not been read here.

Result as recorded by the site and by a held source. The article proves that there are infinitely many triples of coprime $3$-powerful numbers $a,b,c$ with $a+b=c$, for example

$$2^3\cdot3^5\cdot73^3+271^3=919^3 ,$$

and in its construction at least two of $a,b,c$ are perfect cubes. This is the account on the erdosproblems.com page for Problem 939 (last edited 28 May 2026, read 2026-09-27) and in the formal-conjectures docstring of erdos_939.variants.triples; the held Walsh preprint cites the paper as the first solution of the coprime $3$-powerful question. The displayed identity was recomputed here: both summands and the sum are $3$-powerful and the two summands are coprime.

Bears on. Problem 939: answers its third question (infinitely many coprime $3$-powerful $a,b,c$ with $a+b=c$) in the affirmative; a refereed publication.

Read status. Unread; the citation and DOI are bibliographic metadata, and the result statement is consumed through the site's record and Walsh's citation, not from the text.