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arXiv:1708.08085 [math.NT]AbstractReferencesReviewsResources

Valuations, arithmetic progressions, and prime numbers

Shin-ichiro Seki

Published 2017-08-27Version 1

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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