The board / number theory / #43
Erdős Problem #43
DISPROVED LEANdatabase updated 2026-08-23
The statement as posed is false. 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).
Let \(f(N)\) be the maximum possible size of a Sidon set in \(\{1,\ldots,N\}\).
If \(A\) and \(B\) are Sidon sets in \(\{1,\ldots,N\}\) with \((A-A)\cap(B-B)=\{0\}\), is it true that \[\binom{\lvert A\rvert}{2}+\binom{\lvert B\rvert}{2}\leq\binom{f(N)}{2}+O(1)?\] The answer is no; the Erdős Problems page notes that this follows from the solution to Erdős Problem 42.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/43.Attempts
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