Cohn (1998): A conjecture of Erdős on 3-powerful numbers

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J. H. E. Cohn, A conjecture of Erdős on 3-powerful numbers, Mathematics of Computation 67 (1998), no. 221, 439--440, doi:10.1090/S0025-5718-98-00881-3 (bibliographic data from Crossref). The text was not read: the publisher's article PDF at https://www.ams.org/journals/mcom/1998-67-221/S0025-5718-98-00881-3/S0025-5718-98-00881-3.pdf answered HTTP 403 with a browser-check page to every request made on 2026-09-27, so the article's numbering and proof have not been read here.

Result as recorded by the site and by a citing source. The article constructs infinitely many triples of coprime $3$-powerful numbers $a,b,c$ with $a+b=c$ none of which is a perfect cube, strengthening the Nitaj construction, in which at least two of $a,b,c$ are 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 Walsh preprint cites the paper as a second, different solution of the coprime $3$-powerful question.

Bears on. Problem 939: a second affirmative answer to its third question, with the extra property that no term is a cube; 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.