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Erdős problem 818

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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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Problem row
sha256:362227f6429c982d79199c52d730bb0f59e67a9f0c4f8700c9dfdd7114ac4248
Metadata
sha256:24c8f3c5af8ac665e6dc60415c6bee49ef12a80a0a6ff3021e25eaac6588945a
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:fc51a288d1ab538a6fb282af7f0029b485651dc9636540b12053045acf139074
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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