There are no k-Pell numbers expressible as products of two Fermat numbers

Gueyea, Alioune and Rihaneb, Salah Eddine and Togbé, Alain (2025) There are no k-Pell numbers expressible as products of two Fermat numbers. Annales Mathematicae et Informaticae, 62. pp. 77-90. ISSN 1787-5021 (Print) 1787-6117 (Online)

Preview

Text AMI_62_from77to90.pdf - Published Version Download (563kB) | Preview

Abstract

Let k ≥ 2. A generalization of the well-known Pell sequence is the k-Pell sequence. The first k terms of the sequence are 0,...,0,1 and each term afterwards is given by the linear recurrence P(k)n =2P(k)n−1 +P(k)n−2 +···+P(k)n−k. In this paper, we use Baker’s method to determine all the solutions of the Diophnatine equation P(k)n =(2a+1)(2b +1), where a and b are positive integers. Then, we deduce that there are no k-Pell numbers expressible as products of two Fermat numbers.

Actions (login required)

Edit Item