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On the $ p$-divisibility of the Fermat quotients


Author: Wells Johnson
Journal: Math. Comp. 32 (1978), 297-301
MSC: Primary 10A10; Secondary 10A30
DOI: https://doi.org/10.1090/S0025-5718-1978-0463091-4
MathSciNet review: 0463091
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Abstract: Upper bounds for the power of p which divides the Fermat quotient $ {q_a} = ({a^{p - 1}} - 1)/p$ are obtained, and conditions are given which imply that $ {q_a}\nequiv\;0$ $ \pmod p$. The results are in terms of the number of steps in a simple algorithm which determines the semiorder of a $ \pmod p$.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1978-0463091-4
Keywords: Fermat quotients, Fermat's Last Theorem, Wieferich's criterion
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society