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Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

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Claim. Equation (3) of P. Erdős, Számelméleti megjegyzések I, Mat. Lapok 12 (1961), 10–17 (card):

∑p<xn2(p)=(1+o(1))xlog⁡x∑k≥1pk2k,\sum_{p<x}n_2(p)=(1+o(1))\frac{x}{\log x}\sum_{k\ge1}\frac{p_k}{2^k},

where n2(p)n_2(p) is the least quadratic nonresidue modulo pp and p1<p2<⋯p_1<p_2<\cdots are the primes. It answers a question of Mirsky and is proved with Linnik's large sieve together with Brun's sieve and the prime number theorem for progressions.

Covers. The case k=2k=2 of the Statement of Problem 980.

Acceptance. A refereed journal publication (refereed). The curator's PROVED label credits Elliott for the general case, and k=2k=2 is not a part under the parts rule, so the label is not curator credit for this page.

Depends on. No page of this wiki.