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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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