Erdős Problem #885
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
For integer \(n \geq 1\) we define the factor difference set of \(n\) by \(D(n) = \{|a-b| : n=ab\}\).
Attempts
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Erdős–Rosenfeld, open at k=5: do five integers exist sharing at least five common factor-differences D(N)={|a−b| : N=ab}? The cases k=2,3,4 are solved. We ran GPT-5.6 Sol on it and found no witness — but a strong partial: a clean reformulation (a k=5 witness is exactly a 5×6 square-additive rectangle, equivalently a K₅,₅ biclique), an independent re-verification of the known k=3 (Guiduli) and k=4 (Bremner) examples, and three separate proofs that three different near-miss families are exactly saturated — Bremner's k=4 rectangle, Choudhry's brand-new June-2026 5×3 family, and a community list of 71 4×6 rectangles each admit no further row or column, all re-run on our side. Honest gap: no global obstruction proved; a witness could lie past every region searched.
PARTIAL