On multiplicative intersections between the Pell and Jacobsthal numbers
By: Ahmet Daşdemir and Mehmet Varol
References
- Bravo, J. J., C. A. Gómez, and F. Luca. “Powers of Two as Sums of Two k-Fibonacci Numbers.” Miskolc Mathematical Notes 17, no. 1 (2016): 85-100. Cited on 36.
- Daşdemir, A. “On the Pell, Pell-Lucas and Modified Pell Numbers by Matrix Method.” Applied Mathematical Sciences 5, no. 64 (2011): 3173-3181. Cited on 34.
- Daşdemir, A. “A Study on the Jacobsthal and Jacobsthal-Lucas Numbers.” DUFED Journal of Sciences 3, no. 1 (2014): 13-18. Cited on 34.
- Daşdemir, A. “Mersenne, Jacobsthal, and Jacobsthal-Lucas Numbers with Negative Subscripts.” Acta Mathematica Universitatis Comenianae 88, no. 1 (2019): 145-156. Cited on 34.
- Daşdemir, A., and M. Varol. “Lucas Numbers Which Are Products of Two Pell Numbers.” The Fibonacci Quarterly 63, no. 1 (2025): 78-83. Cited on 34.
- Ddamulira, M., F. Luca, and M. Rakotomalala. “Fibonacci Numbers Which Are Products of Two Pell Numbers.” The Fibonacci Quarterly 54, no. 1 (2016): 11-18. Cited on 34.
- Ddamulira, M., C. A. Gómez, and F. Luca. “On a Problem of Pillai with k- Generalized Fibonacci Numbers and Powers of 2.” Monatshefte für Mathematik 187, no. 4 (2018): 635-664. Cited on 34.
- Dujella, A., and A. Pethő. “A Generalization of a Theorem of Baker and Davenport.” The Quarterly Journal of Mathematics 49, no. 195 (1998): 291-306. Cited on 36.
- Emin, A. “On the Diophantine Equation
[L_m^2 + L_n^2 = 2^a - Emin, A. “On the Dynamics of the Fermat-like Diophantine Equation Involving Pell Numbers.” AIMS Mathematics 10, no. 8 (2025): 18524-18540. Cited on 34.
- Faye, B., F. Luca, S. E. Rihane, and A. Togbé. “The Diophantine Equations
P_n^x + P_{n+1}^y = P_m^x \quad \text{or} \quad P_n^y + P_{n+1}^x = P_m^x[ - Gómez, C. A., J. C. Gómez, and F. Luca. “On the Exponential Diophantine
[F_{n+1}^x - F_{n-1}^x = F_m^y - Gueye, A., S. E. Rihane, and A. Togbé. “An Exponential Equation Involving k- Fibonacci Numbers.” Turkish Journal of Mathematics 45, no. 6 (2021): 2664-2677. Cited on 34.
- Kılıç, E., and D. Taşçı. “The Linear Algebra of the Pell Matrix.” Boletín de la Sociedad Matemática Mexicana, ser. 3, 11, no. 2 (2005): 163-174. Cited on 34.
- Koshy, T. Elementary Number Theory with Applications. New York: Harcourt Academic Press, 2002. Cited on 33.
- Matveev, E. M. “An Explicit Lower Bound for a Homogeneous Rational Linear Form in the Logarithms of Algebraic Numbers. II.” Izvestiya: Mathematics 64, no. 6 (2000): 1217-1269. Cited on 36.
- Pongsriiam, P. “Fibonacci and Lucas Numbers Which Are One Away from Their Products.” The Fibonacci Quarterly 55, no. 1 (2017): 29-40. Cited on 34.
- Rihane, S. E., B. Faye, F. Luca, and A. Togbé. “On the Exponential Diophantine
[P_n^x + P_{n+1}^x = P_m - Rihane, S. E., Y. Akrour, and A. El Habibi. “Fibonacci Numbers Which Are Products of Three Pell Numbers and Pell Numbers Which Are Products of Three Fibonacci Numbers.” Boletín de la Sociedad Matemática Mexicana 26, no. 3 (2020): 895-910. Cited on 34.
- Vajda, S. Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. New York: Courier Corporation, 2008. Cited on 33.
- Waldschmidt, M. Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential Function in Several Variables. Berlin: Springer, 2000. Cited on 35.
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
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© 2026 Ahmet Daşdemir, Mehmet Varol, published by Pedagogical University of Cracow
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