Non-Wieferich primes in arithmetic progressions Article Swipe

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YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.1090/proc/13201

Graves and Murty proved that for any integer $a\ge 2$ and any fixed integer $k\ge 2$, there are $\gg \log x/\log \log x$ primes $p\le x$ such that $a^{p-1}\not \equiv 1\pmod {p^2}$ and $p\equiv 1\pmod k$, under the assumption of the abc conjecture. In this paper, for any fixed $M$, the bound $\log x/\log \log x$ is improved to $(\log x/\log \log x) (\log \log \log x)^M$.

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Integer (computer science) Log-log plot Mathematics Combinatorics Conjecture Binary logarithm Arithmetic Discrete mathematics Computer science Programming language

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Type: article
Language: en
Landing Page: https://doi.org/10.1090/proc/13201
PDF: https://www.ams.org/proc/2017-145-05/S0002-9939-2017-13201-8/S0002-9939-2017-13201-8.pdf
OA Status: bronze
Cited By: 9
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DOI: https://doi.org/10.1090/proc/13201

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Title: Non-Wieferich primes in arithmetic progressions

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Type: article

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Language: en

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Publication year: 2016

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Publication date: 2016-03-24

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Authors: Yong-Gao Chen, Yuchen Ding

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Landing page: https://doi.org/10.1090/proc/13201

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PDF URL: https://www.ams.org/proc/2017-145-05/S0002-9939-2017-13201-8/S0002-9939-2017-13201-8.pdf

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Concepts: Integer (computer science), Log-log plot, Mathematics, Combinatorics, Conjecture, Binary logarithm, Arithmetic, Discrete mathematics, Computer science, Programming language

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Cited by: 9

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