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Claim. A. Bremner, On a problem of Erdős related to common factor differences, Int. J. Number Theory 15 (2019), no. 5, 1059--1068, proves that there are infinitely many sets of four integers with four common factor differences, as the paper's abstract states. This answers Problem 885 yes for $k=4$. The abstract presents the result as an extension of the ideas of Jiménez-Urroz's paper (claim page), which settles $k=3$. The page is dated by the paper's online publication.

Covers. The instance $k=4$.

Depends on. No page of this wiki.

Acceptance. Refereed: International Journal of Number Theory. The site labels the problem OPEN, so its commentary crediting the paper is not acceptance.