Irmak, NurettinLiptai, KalmanSzalay, Laszlo2024-11-072024-11-0720181331-0623https://hdl.handle.net/11480/15661In this paper, we solve a few Diophantine equations linked to balancing numbers and factorials. The basic problem consists of solving the equation B-y = x! in positive integers x, y, which has only one nontrivial solution B-2 = 6 = 3!, as a direct consequence of the theorem of F. Luca [5]. A more difficult problem is to solve B-y = x(2)!/x(1)!, but we were able to handle it under some conditions. Two related problems are also studied.eninfo:eu-repo/semantics/closedAccessFactorialsbalancing numbersdiophantine equationArticle2321972042-s2.0-85059092588Q3WOS:000443101100004Q2