Erdős Problem a Daythe open tracker

Erdős Problem #888

SOLVED LEANdatabase updated 2026-08-23

Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways. A solution has also been checked by machine, in Lean.

What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).

Condition on the sets \(A\) appearing in Erdős 888. Namely, let \(A\) be a subset of \({1,...,n}\) such that if \(a ≤ b ≤ c ≤ d ∈ A\) and \(abcd\) square then \(ad=bc\).

Proposition that for a specific \(n\) an \(A\) with the above defined condition and cardinality \(k\) exists.

What is the size of the largest \(A\subseteq \{1,\ldots,n\}\) such that if \(a\leq b\leq c\leq d\in A\) are such that \(abcd\) is a square then \(ad=bc\)? This was proved by GPT-5.5 Pro (prompted by Chojecki).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/888.
Prizenone
Topicsnumber theory, squares
Statement in LeanFormal Conjectures
Solution in Leanyes
OEISA387584
Original pageerdosproblems.com/888
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