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Chebyshevskii Sb., 2014, Volume 15, Issue 4, Pages 124–138 (Mi cheb361)  

On some Diophantine equation with variables from lacunar sequence

V. N. Chubarikova, N. M. Dobrovolskiyb

a Lomonosov Moscow State University
b Tula State Pedagogical University

Abstract: By M. P. Mineev's method of basic and auxiliary systems, we prove a theorem on a number of solutions of some inhomogeneous Diophantine equation with variables from a lacunar sequence of natural numbers.
Using Bernoulli numbers, we obtain a polynomial-type expression for the number of basic systems. The estimates for the number of auxiliary systems are also given.
Bibliography: 12 titles.

Keywords: Diophantine equation, gap sequence.

Full text: PDF file (246 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 519.2+511
Received: 05.12.2014

Citation: V. N. Chubarikov, N. M. Dobrovolskiy, “On some Diophantine equation with variables from lacunar sequence”, Chebyshevskii Sb., 15:4 (2014), 124–138

Citation in format AMSBIB
\Bibitem{ChuDob14}
\by V.~N.~Chubarikov, N.~M.~Dobrovolskiy
\paper On some Diophantine equation with variables from lacunar sequence
\jour Chebyshevskii Sb.
\yr 2014
\vol 15
\issue 4
\pages 124--138
\mathnet{http://mi.mathnet.ru/cheb361}


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