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Revision difference : Wieferich prime |
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| 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. |
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. |
| \begin{thebibliography}{9} |
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| \bibitem{IR} Ireland, Kenneth and Rosen, Michael. A Classical Introduction to Modern Number Theory. Springer, 1998. |
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| \bibitem{Na} Nathanson, Melvyn B. Elementary Methods in Number Theory. Springer, 2000. |
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| \end{thebibliography} |
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