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Erdős problem 818

Let AA be a finite set of integers such that ∣A+A∣≪∣A∣\lvert A+A\rvert \ll \lvert A\rvert. Is it true that ∣AA∣≫∣A∣2(log⁡∣A∣)C\lvert AA\rvert \gg \frac{\lvert A\rvert^2}{(\log \lvert A\rvert)^C} for some constant C>0C>0?

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sha256:362227f6429c982d79199c52d730bb0f59e67a9f0c4f8700c9dfdd7114ac4248
Metadata
sha256:24c8f3c5af8ac665e6dc60415c6bee49ef12a80a0a6ff3021e25eaac6588945a
Observation
sha256:8c823d621b7e1256c8e47c60a5f1c54c016a5507e6f27b2bab537f6f5f232067
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sha256:fc51a288d1ab538a6fb282af7f0029b485651dc9636540b12053045acf139074
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sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
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sha256:c9d14c459c518937e758918b5897dc3b22f1a55f07739afe99502f5b046c907a
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2415f78e850aeee50afdca525c6f2e0ea606f207
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