FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS

Ahmet Daşdemir; Ahmet Emin

doi:10.18038/estubtda.1444927

EN

FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS

Abstract

This study presents all solutions to the Diophantine equations F_k=L_m L_n and L_k=F_m F_n. To be clear, the Fibonacci numbers that are the product of two arbitrary Lucas numbers and the Lucas numbers that are the product of two arbitrary Fibonacci numbers are determined herein. The results under consideration are proven by using the Dujella-Pethő lemma in coordination with Matveev's theorem. All common terms of the Fibonacci and Lucas numbers are determined. Further, the Lucas-square Fibonacci and Fibonacci-square Lucas numbers are given.

Keywords

Fibonacci and Lucas numbers, logarithmic height in logarithms, Matveev theorem, Dujella and Pethö lemma

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Ahmet Daşdemir
0000-0001-8352-2020
Türkiye

Ahmet Emin ^*
0000-0001-7791-7181
Türkiye

Publication Date

September 30, 2024

Submission Date

February 29, 2024

Acceptance Date

July 3, 2024

Published in Issue

Year 2024 Volume: 25 Number: 3

DOI

https://doi.org/10.18038/estubtda.1444927

IZ

https://izlik.org/JA43EG83MW

APA

Daşdemir, A., & Emin, A. (2024). FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, 25(3), 407-414. https://doi.org/10.18038/estubtda.1444927

AMA

1.Daşdemir A, Emin A. FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS. Estuscience - Se. 2024;25(3):407-414. doi:10.18038/estubtda.1444927

Chicago

Daşdemir, Ahmet, and Ahmet Emin. 2024. “FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 25 (3): 407-14. https://doi.org/10.18038/estubtda.1444927.

EndNote

Daşdemir A, Emin A (September 1, 2024) FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 25 3 407–414.

IEEE

[1]A. Daşdemir and A. Emin, “FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS”, Estuscience - Se, vol. 25, no. 3, pp. 407–414, Sept. 2024, doi: 10.18038/estubtda.1444927.

ISNAD

Daşdemir, Ahmet - Emin, Ahmet. “FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 25/3 (September 1, 2024): 407-414. https://doi.org/10.18038/estubtda.1444927.

JAMA

1.Daşdemir A, Emin A. FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS. Estuscience - Se. 2024;25:407–414.

MLA

Daşdemir, Ahmet, and Ahmet Emin. “FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 25, no. 3, Sept. 2024, pp. 407-14, doi:10.18038/estubtda.1444927.

Vancouver

1.Ahmet Daşdemir, Ahmet Emin. FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS. Estuscience - Se. 2024 Sep. 1;25(3):407-14. doi:10.18038/estubtda.1444927

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