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

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 \(F\)\(n\) = \(a\)2\(n\) + 1 for \(a\); \(n\) \(ε\) \(Z\) and \(n\) \(≥\) 0 and as a result of these recurrent relations, to get some properties of divisibility for generalized Fermat numbers.