ON SOME DIOPHANTINE EQUATION WITH VARIABLES FROM LACUNAR SEQUENCE
https://doi.org/10.22405/2226-8383-2014-15-4-124-138
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.
About the Authors
V. N. Chubarikov
Московский государственный университет имени М. В. Ломоносова.
Russian Federation
Russian Federation
N. M. Dobrovolskiy
Тульский государственный педагогический университет им. Л. Н. Толстого
Russian Federation
Russian Federation
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Review
For citations:
Chubarikov V.N., Dobrovolskiy N.M. ON SOME DIOPHANTINE EQUATION WITH VARIABLES FROM LACUNAR SEQUENCE. Chebyshevskii Sbornik. 2014;15(4):124-138. (In Russ.) https://doi.org/10.22405/2226-8383-2014-15-4-124-138
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