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Erdős problem 33

Let A ⊆ ℕ be a set such that every integer can be written as n^2 + a for some a in A and n ≥ 0. What is the smallest possible value of lim sup n → ∞ |A ∩ {1, …, N}| / N^(1/2)?

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sha256:1781d73fab517c5d2f3e346eef7c7bfe276b15f6a4421785a2d2f57109cfa62c
Metadata
sha256:958dc234c908bbe0db4693ac42568b699ab2073ce29441124b4586e11c9b54f1
Observation
sha256:8c823d621b7e1256c8e47c60a5f1c54c016a5507e6f27b2bab537f6f5f232067
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sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
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sha256:c9d14c459c518937e758918b5897dc3b22f1a55f07739afe99502f5b046c907a
Source commit
2415f78e850aeee50afdca525c6f2e0ea606f207
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