On some Diophantine equation with variables from lacunar sequence

V. N. Chubarikov^a, N. M. Dobrovolskiy<sup>b

a</sup> 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.

UDC: 519.2+511

Received: 05.12.2014