The board / sidon sets / #153
Erdős Problem #153
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Define \(f(n)\) to be the minimum of \(\frac{1}{t}\sum_{1\leq i<t}(s_{i+1}-s_i)^2\) as \(A\) ranges over all Sidon sets of size \(n\), where \(A+A=\{s_1<\cdots<s_t\}\).
Let \(A\) be a finite Sidon set and \(A+A=\{s_1<\cdots<s_t\}\). Is it true that \[\frac{1}{t}\sum_{1\leq i<t}(s_{i+1}-s_i)^2 \to \infty\] as \(\lvert A\rvert\to \infty\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/153.Prizenone
Topicssidon sets
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/153
Attempts
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