Problem 818

Let $A$ be a finite set of integers such that $\lvert A+A\rvert \ll \lvert A\rvert$ . Is it true that

\lvert AA\rvert \gg \frac{\lvert A\rvert^2}{(\log \lvert A\rvert)^C}

for some constant $C>0$ ?

Source: erdosproblems.com/818

Additive combinatorics

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SolvedProved

An accepted solution exists. The statement is true.

Proved: the site labels the problem PROVED (LEAN); the corpus has not built the Lean proof, so it gives no formal evidence. The standing is derived from the claim page (Solymosi, 2008), accepted on the refereed publication and the site's credit.

Problem 818

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Proof claims

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