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Erdős problem / erdos

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Problem 40

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  1. vf_e5951913fd90d2a4

    theoretical

    Erdős Problem #40: declared status 'open'. Formalized: yes. For what functions g(N)→∞g(N)\to \infty is it true that∣A∩{1,…,N}∣≫N1/2g(N)\lvert A\cap \{1,\ldots,N\}\rvert \gg \frac{N^{1/2}}{g(N)}implies lim sup⁡1A∗1A(n)=∞\limsup 1_A\ast 1_A(n)=\infty? Prize: $500. Tags: additive basis, number theory.

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