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'Wieferich prime'
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| Title of object: |
Wieferich prime |
| Canonical Name: |
WieferichPrime |
| Type: |
Definition |
| Created on: |
2003-08-11 14:32:09 |
| Modified on: |
2003-08-11 14:32:09 |
Revision comment (for changes between this and next version):
| Changes for correction #2377 ('Classification?'). |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
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\usepackage{amssymb}
\usepackage{amsmath}
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\usepackage{amsthm}
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%\usepackage{psfrag}
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%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
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%\usepackage{xypic}
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% define commands here
\newcommand{\mc}{\mathcal}
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\newcommand{\ol}{\overline}
\newcommand{\ra}{\rightarrow}
\newcommand{\la}{\leftarrow}
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\newcommand{\Ra}{\Rightarrow}
\newcommand{\nor}{\vartriangleleft}
\newcommand{\Gal}{\text{Gal}}
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\newcommand{\<}{\langle}
\renewcommand{\>}{\rangle} |
Content:
| By Fermat's little theorem the relationship $p\mid2^p-1$ for any odd prime $p$. An odd prime $p$ such that $p^2\nmid 2^p-1$ is called a Wieferich prime. It is currently unknown whether or not there are infinitely many Wieferich primes, or whether or not there are infinitely many primes that are not Wieferich, though the ABC conjecture implies the former. |
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