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Combinatorics
Erdős problem 153
Let A be a finite Sidon set and A+A={s1<⋯<st}
. Is it true that
t11≤i<t∑(si+1−si)2→∞
as
∣A∣→∞
?
$2,690 bounty·1 piece from 1 person·last one 12 days ago
week of 27 Sept 2025 · nothing publishedweek of 4 Oct 2025 · nothing publishedweek of 11 Oct 2025 · nothing publishedweek of 18 Oct 2025 · nothing publishedweek of 25 Oct 2025 · nothing publishedweek of 1 Nov 2025 · nothing published
Solve it
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
27 Sept 2025a year of work on this problem19 Sept 2026
erdosproblems.com/153
[ESS94] Erdős, P. and Sárközy, A. and Sós, T., On Sum Sets of Sidon Sets, I. Journal of Number Theory (1994), 329-347.
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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