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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 242, Pages 98–102 (Mi tm407)  
A Diophantine Representation of Bernoulli Numbers and Its Applications

Yu. V. Matiyasevich

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
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Abstract: A new method for constructing a Diophantine representation of Bernoulli numbers is proposed. The method is based on the Taylor series for the function $\tau /(e^\tau -1)$. This representation can be used for constructing Diophantine representations of the set of all Carmichael numbers (i.e. numbers that are pseudoprime for every base) and for the set of all square-free numbers.
Received in October 2002
Bibliographic databases:
UDC: 510.6+511
Language: Russian
Citation: Yu. V. Matiyasevich, “A Diophantine Representation of Bernoulli Numbers and Its Applications”, Mathematical logic and algebra, Collected papers. Dedicated to the 100th birthday of academician Petr Sergeevich Novikov, Trudy Mat. Inst. Steklova, 242, Nauka, MAIK «Nauka/Inteperiodika», M., 2003, 98–102; Proc. Steklov Inst. Math., 242 (2003), 86–91
Citation in format AMSBIB
\Bibitem{Mat03}
\by Yu.~V.~Matiyasevich
\paper A~Diophantine Representation of Bernoulli Numbers and Its Applications
\inbook Mathematical logic and algebra
\bookinfo Collected papers. Dedicated to the 100th birthday of academician Petr Sergeevich Novikov
\serial Trudy Mat. Inst. Steklova
\yr 2003
\vol 242
\pages 98--102
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm407}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2054487}
\zmath{https://zbmath.org/?q=an:1118.11013}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2003
\vol 242
\pages 86--91
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