Geodesic
On some Diophantine equation with variables from lacunar sequence
Čebyševskij sbornik, Tome 15 (2014) no. 4, pp. 124-138

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{CHEB_2014_15_4_a3,
     author = {V. N. Chubarikov and N. M. Dobrovolskiy},
     title = {On some {Diophantine} equation with variables from lacunar sequence},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {124--138},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2014_15_4_a3/}
}
TY  - JOUR
AU  - V. N. Chubarikov
AU  - N. M. Dobrovolskiy
TI  - On some Diophantine equation with variables from lacunar sequence
JO  - Čebyševskij sbornik
PY  - 2014
SP  - 124
EP  - 138
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2014_15_4_a3/
LA  - ru
ID  - CHEB_2014_15_4_a3
ER  - 
%0 Journal Article
%A V. N. Chubarikov
%A N. M. Dobrovolskiy
%T On some Diophantine equation with variables from lacunar sequence
%J Čebyševskij sbornik
%D 2014
%P 124-138
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2014_15_4_a3/
%G ru
%F CHEB_2014_15_4_a3
V. N. Chubarikov; N. M. Dobrovolskiy. On some Diophantine equation with variables from lacunar sequence. Čebyševskij sbornik, Tome 15 (2014) no. 4, pp. 124-138. http://geodesic.mathdoc.fr/item/CHEB_2014_15_4_a3/