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Zap. Nauchn. Sem. LOMI, 1977, Volume 67, Pages 167–183 (Mi znsl2015)  

This article is cited in 2 scientific papers (total in 2 papers)

A class of primality criteria formulated in terms of the divisibility of binomial coefficients

Yu. V. Matiyasevich


Abstract: We find a class of theorems of the type “$q$ is a prime number iff $R(g)$ is a divisor of the binomial coefficient $\begin{pmatrix}S(q)
T(q)\end{pmatrix}$
”; here $R$, $S$, $T$ are certain fully significant functions that are superpositions of addition, subtraction, multiplication, division, and raising to a power. Similar criteria were also obtained for prime Mersenne numbers, prime Fermat numbers, and twin-prime numbers.

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English version:
Journal of Soviet Mathematics, 1981, 16:1, 874–885

Bibliographic databases:

UDC: 511

Citation: Yu. V. Matiyasevich, “A class of primality criteria formulated in terms of the divisibility of binomial coefficients”, Studies in number theory. Part 4, Zap. Nauchn. Sem. LOMI, 67, "Nauka", Leningrad. Otdel., Leningrad, 1977, 167–183; J. Soviet Math., 16:1 (1981), 874–885

Citation in format AMSBIB
\Bibitem{Mat77}
\by Yu.~V.~Matiyasevich
\paper A class of primality criteria formulated in terms of the divisibility of binomial coefficients
\inbook Studies in number theory. Part~4
\serial Zap. Nauchn. Sem. LOMI
\yr 1977
\vol 67
\pages 167--183
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2015}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=463098}
\zmath{https://zbmath.org/?q=an:0453.10005|0355.10003}
\transl
\jour J. Soviet Math.
\yr 1981
\vol 16
\issue 1
\pages 874--885
\crossref{https://doi.org/10.1007/BF01213897}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. S. Marchenkov, “Superpositions of elementary arithmetic functions”, J. Appl. Industr. Math., 1:3 (2007), 351–360  mathnet  crossref  mathscinet  zmath
    2. Yu. V. Matiyasevich, “Gipoteza Rimana kak chetnost spetsialnykh binomialnykh koeffitsientov”, Chebyshevskii sb., 19:3 (2018), 46–60  mathnet  crossref  elib
  • Записки научных семинаров ПОМИ
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