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Erdős problem 749

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Let ϵ>0\epsilon>0. Does there exist A⊆NA\subseteq \mathbb{N} such that the lower density of A+AA+A is at least 1−ϵ1-\epsilon and yet 1A∗1A(n)≪ϵ11_A\ast 1_A(n) \ll_\epsilon 1 for all nn?

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Problem row
sha256:b7fa87d2fb8e8704d1e7b4f2271ccfab355e5305754eab421471e0e501c02991
Metadata
sha256:3d2f5fb2caebe0935ef289ed279dd205e0bc733743e6300834efefc9610f6f08
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:82a1c77e18f055db793e0d086fbab34297ed643a04fc2d895bf5ef6123a42317
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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