On multiplicative intersections between the Pell and Jacobsthal numbers

Ahmet Daşdemir; Mehmet Varol

doi:10.2478/aupcsm-2026-0003

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On multiplicative intersections between the Pell and Jacobsthal numbers

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 26 (2026): Issue 1 (December 2026)

By: Ahmet Daşdemir and Mehmet Varol

Open Access

|Nov 2026

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Abstract

We determine all integer triples (k, m, n) satisfying the Diophantine equations P_k = J_mJ_n and J_k = P_mP_n, thereby characterizing Pell numbers that are products of two Jacobsthal numbers, and vice versa. In addition, we study the intersection of the Pell and Jacobsthal sequences and show that the only common values occur when m = 1, corresponding to the integers 1 and 5.

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Articles in this issue

DOI: https://doi.org/10.2478/aupcsm-2026-0003 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 33 - 42

Submitted on: Feb 9, 2026

Accepted on: Jul 16, 2026

Published online: Nov 3, 2026

Published in print: Dec 1, 2026

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Keywords:

Pell number,

Jacobsthal number,

linear form in logarithm,

reduction method,

Diophantine equation

MSC:

11B39,

11J86

Related subjects:

Mathematics,

General mathematics

© 2026 Ahmet Daşdemir, Mehmet Varol, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 26 (2026): Issue 1 (December 2026)