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Erdős problem 52

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Let AA be a finite set of integers. Is it true that for every ϵ>0\epsilon>0 max⁡(∣A+A∣,∣AA∣)≫ϵ∣A∣2−ϵ?\max( \lvert A+A\rvert,\lvert AA\rvert)\gg_\epsilon \lvert A\rvert^{2-\epsilon}?

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Problem row
sha256:37c3f641e7f1369a2d3fe7bb009d196d66199a5e7abe88fae78f2233e209b541
Metadata
sha256:fd9423a6106c7255971b13e20e8cea5ebdabbbc0140dc22f2d727cdec7c592b3
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:404e277b67f1c4e57eb01969c0adeae7f4d949f862ece2c35d13d28ac978af8a
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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