Factorial-like values in the balancing sequence

Nurettin Irmak; Kálmán Liptai; László Szalay

Vol. 23 No. 2 (2018)

Regular Articles

Factorial-like values in the balancing sequence

Published 2017-12-13

Nurettin Irmak
Kálmán Liptai
László Szalay

Nurettin Irmak
Ömer Halisdemir University

Kálmán Liptai
University of Eger

László Szalay
J. Selye University and University of West Hungary.

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Abstract

In this paper, we solve a few diophantine equations linked to balancing numbers and factorials. The basic problem $B_y=x!$ has only the one nontrivial solution $B_2=6=3!$, but it is a direct consequence of a theorem of F.~Luca. The more difficult problem $B_y=x_2!/x_1!$ is still open, but we solve it under different conditions. Two related problems are also studied.

Keywords

Factorials, balancing numbers, diophantine equation

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Author Biography

Nurettin Irmak

Mathematics Department

Kálmán Liptai

Institute of Mathematics and Informatics

László Szalay

Institute of Mathematics.