On Some Recurrence Relations Connected with Generalized Fermat Numbers and Some Properties of Divisibility for these Numbers

Abstract

As a result of nice properties of Fermat numbers and their interesting applications, these numbers have recently seen a variety of developments and extensions. Within this framework, this paper contributes. The purpose of this paper is to obtain some recurrence relations connected with generalized Fermat numbers \(\mathcal{F}\)\(\mathcal{n}\) = \(\mathcal{a}\)2\(\mathcal{n}\) + 1 for \(\mathcal{a}\), \(\mathcal{n}\) \(\epsilon\) \(\mathbb{Z}\) and \(\mathcal{n}\) \(\geq\) 0 and as a result of these recurrent relations, to get some properties of divisibility for generalized Fermat numbers.