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arXiv · 1708.08085

Valuations, arithmetic progressions, and prime numbers

Shin-ichiro Seki
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Abstract

In this short note, we give two proofs of the infinitude of primes via valuation theory and give a new proof of the divergence of the sum of prime reciprocals by Roth's theorem and Euler-Legendre's theorem for arithmetic progressions.

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Shin-ichiro Seki. 2018-02-12. Valuations, arithmetic progressions, and prime numbers. https://arxiv.org/abs/1708.08085

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