When does (P x n+1 +P x n−1 )/2 Equal a Pell-Lucas Number?

Djamel Bellaouar

When does (P x n+1 +P x n−1 )/2 Equal a Pell-Lucas Number?

Authors

Djamel Bellaouar

Keywords:

Exponential diophantine equations; Pell numbers; Pell-Lucas numbers; Linear forms in logarithms.

Abstract

In the present paper, we will find all solutions (m,n,x) for the equation P^x_n+1+P^x_n−1 = 2Q_m, where P_i is the i-th term of Pell sequence and Q_i is the i-th term of Pell-Lucas sequence.

Keywords: Exponential diophantine equations; Pell numbers; Pell-Lucas numbers; Linear forms in logarithms.

2020 Mathematics Subject Classification. 11B39; 11J86; 11D72

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Published

2025-10-13

How to Cite

Djamel Bellaouar. (2025). When does (P x n+1 +P x n−1 )/2 Equal a Pell-Lucas Number?. Jordan Journal of Mathematics and Statistics, 18(3), 341–349. Retrieved from https://jjms.yu.edu.jo/index.php/jjms/article/view/1414