On the diophantine equations Jₙ + Jₘ = Lₖ and Lₙ + Lₘ = Jₖ

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Published: 2026-01-07
DOI: https://doi.org/10.56947/gjom.v22i1.3814
Keywords:
Lucas sequence, Jacobsthal sequence, Linear forms in logarithms

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Osama Salah
Department of Mathematics, Faculty of Science, Ain Shams University, Egypt
Ahmed Elsonbaty
Department of Mathematics, Faculty of Science, Ain Shams University, Egypt
Mohamed Anwar
Department of Mathematics, Faculty of Science, Ain Shams University, Egypt
Mohammed Abd-El Azim Seoud
Department of Mathematics, Faculty of Science, Ain Shams University, Egypt

Abstract

This study contains Lucas numbers that are sums of two Jacobsthal numbers and Jacobsthal numbers that are sums of two Lucas numbers. Our main conclusions are confirmed by a refinement of Baker's theorem for linear forms in logarithms and the reduction method of Dujella and Petho's.

Article Details

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Vol. 22 No. 1 (2026)

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Articles

How to Cite

On the diophantine equations Jₙ + Jₘ = Lₖ and Lₙ + Lₘ = Jₖ. (2026). Gulf Journal of Mathematics, 22(1), 1-15. https://doi.org/10.56947/gjom.v22i1.3814