Problem 154

Let $A\subset \{1,\ldots,N\}$ be a Sidon set with $\lvert A\rvert\sim N^{1/2}$ . Must $A+A$ be well-distributed over all small moduli? In particular, must about half the elements of $A+A$ be even and half odd?

Source: erdosproblems.com/154

Sidon sets

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Status

SolvedProved

An accepted solution exists. The statement is true.

PROVED (LEAN), the site's label. The standing rests on two accepted claim pages: Lindström 1998, the refereed equidistribution of $A$ itself in residue classes, from which the statement for $A+A$ follows by the Sidon property, and its refereed quantitative strengthening Kolountzakis 1999. The label's Lean qualification dates from Wouter van Doorn's formalization of the statement for $A$ , posted to the site's thread on 2026-02-06; a formal derivation of the sumset statement from it followed on 2026-06-27. Both are linked from Lindström's page, and neither has been built or audited in this corpus.

Problem 154

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Proof claims

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