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Matematicheskie Zametki, 2012, Volume 92, Issue 1, Pages 116–122
DOI: https://doi.org/10.4213/mzm9484 (Mi mzm9484) 		 
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
Full-text PDF (440 kB) Citations (1) English version article
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DOI: https://doi.org/10.4213/mzm9484
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.
Received: 19.05.2011
English version:
Mathematical Notes, 2012, Volume 92, Issue 1, Pages 108–114
DOI: https://doi.org/10.1134/S0001434612070127
Bibliographic databases:
Document Type: Article
UDC: 517.172
Language: Russian
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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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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