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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On large Zsigmondy primes


Author: Walter Feit
Journal: Proc. Amer. Math. Soc. 102 (1988), 29-36
MSC: Primary 11A41
MathSciNet review: 915710
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Abstract: If $ a$ and $ m$ are integers greater than 1, then a large Zsigmondy prime is a prime $ l$ such that $ l\left\vert {{a^m} - 1,l\nmid {a^i} - 1} \right.$ for $ 1 \leqslant i \leqslant m - 1$ and either $ {l^2}\left\vert {{a^m} - 1} \right.$ or $ l > m + 1$. The main result of this paper lists all the pairs $ \left( {a,m} \right)$ for which no large Zsigmondy prime exists.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0915710-1
PII: S 0002-9939(1988)0915710-1
Article copyright: © Copyright 1988 American Mathematical Society