SU\G(𝔾)/K·U

Valuations, arithmetic progressions, and prime numbers

Shin-ichiro Seki

Type: Article

Publication Date: 2018-12-01

Citations: 3

DOI: https://doi.org/10.7546/nntdm.2018.24.4.128-132

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.

Locations

  • Notes on Number Theory and Discrete Mathematics - View - PDF
  • arXiv (Cornell University) - View - PDF

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Works Cited by This (5)

Action Title Year Authors
+ PDF Chat Winding quotients and some variants of Fermat's Last Theorem. 1997 Henri Darmon
+ On sets of integers containing no four elements in arithmetic progression 1969 Endre Szemerédi
+ van der Waerden and the Primes 2015 Levent Alpöge
+ History of the theory of numbers 1919 L. E. Dickson
+ The Thirteen Books of Euclid's Elements 1909 G. B. M.