Original scientific paper

Factorial-like values in the balancing sequence

Nurettin Irmak
Kálmán Liptai
László Szalay

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

Hrčak ID:

198689

URI

https://hrcak.srce.hr/198689

Publication date:

7.11.2018.

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