Valuations, arithmetic progressions, and prime numbers
Number Theory
2018-02-13 v2
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.
Cite
@article{arxiv.1708.08085,
title = {Valuations, arithmetic progressions, and prime numbers},
author = {Shin-ichiro Seki},
journal= {arXiv preprint arXiv:1708.08085},
year = {2018}
}