Diophantine Equations Related with Linear Binary Recurrences

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Kilic Emrah; Akkus Ilker; Omur Nese

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Journal Paper

Paper Information

Journal: Iranian Journal of Mathematical Sciences and Informatics Year:2022 | Volume:17 | Issue:1 Page(s): 11-26

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Title

Diophantine Equations Related with Linear Binary Recurrences

Author(s)

Kilic Emrah | Akkus Ilker | Omur Nese | Issue Writer Certificate

Keywords

Linear recurrences

Generalized Fibonacci and Lucas sequences

Diophantine equations

Continued fractions

Abstract

In this paper we nd all solutions of four kinds of the Diophantine equations x2 Vtxy 􀀀 y2 x = 0 and x2 Vtxy 􀀀 y2 y = 0; for an odd number t, and, x2 Vtxy + y2 􀀀 x = 0 and x2 Vtxy + y2 􀀀 y = 0; for an even number t, where Vn is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh.

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APA: Copy

Kilic, Emrah, Akkus, Ilker, & Omur, Nese. (2022). Diophantine Equations Related with Linear Binary Recurrences. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 17(1), 11-26. SID. https://sid.ir/paper/990695/en

Vancouver: Copy

Kilic Emrah, Akkus Ilker, Omur Nese. Diophantine Equations Related with Linear Binary Recurrences. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2022;17(1):11-26. Available from: https://sid.ir/paper/990695/en

IEEE: Copy

Emrah Kilic, Ilker Akkus, and Nese Omur, “Diophantine Equations Related with Linear Binary Recurrences,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 17, no. 1, pp. 11–26, 2022, [Online]. Available: https://sid.ir/paper/990695/en

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