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Erdős problem 39

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Is there an infinite Sidon set A⊂NA\subset \mathbb{N} such that ∣A∩{1…,N}∣≫ϵN1/2−ϵ\lvert A\cap \{1\ldots,N\}\rvert \gg_\epsilon N^{1/2-\epsilon} for all ε>0\varepsilon > 0?

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Problem row
sha256:cf1d62faa8478e41d3dedecba1b6e6a2460d2d3bd4cf6e1b85bbe0ca3999d159
Metadata
sha256:09d83ce12c0f9948d2cf9024f3aa6480a203ec3a4443a2ce9d5d02b33e3f7474
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:ba6f57ae97fa5b1fc1799e5c58342f59a51cfbf5f4298a8fa59d6abee20ccfc0
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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