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Mat. Zametki, 2012, Volume 92, Issue 1, Pages 116–122 (Mi mz9484)  

This article is cited in 1 scientific paper (total in 1 paper)

Divisibility of Fermat Quotients

Yu. N. Shteinikov

M. V. Lomonosov Moscow State University

Abstract: For any $\varepsilon >0$ and all primes $p$, with the exception of primes from a set with relative zero density, there exists a natural number $a\le(\log p)^{3/2+\varepsilon}$ for which the congruence $a^{p-1}\equiv 1  (\operatorname{mod} p^{2})$ does not hold.

Keywords: Fermat quotient, smooth number, coset, oriented graph

DOI: https://doi.org/10.4213/mzm9484

Full text: PDF file (440 kB)
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English version:
Mathematical Notes, 2012, 92:1, 108–114

Bibliographic databases:

UDC: 517.172
Received: 19.05.2011

Citation: Yu. N. Shteinikov, “Divisibility of Fermat Quotients”, Mat. Zametki, 92:1 (2012), 116–122; Math. Notes, 92:1 (2012), 108–114

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. T. Cochrane, D. De Silva, Ch. Pinner, “$(p-1)$th roots of unity $mod  p^n$, generalized Heilbronn sums, Lind-Lehmer constants, and Fermat quotients”, Mich. Math. J., 66:1 (2017), 203–219  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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