Article detail · 2024 · article
Fibonacci and Lucas Numbers as Products of Their Arbitrary Terms
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- YÖKSİSYÖKSİS article record
- YÖKSİS venueEskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering
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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.
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Citations
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2citationsOpenAlex · cited_by_count (cache / database)
3 publications in the local catalog that cite this work (OpenAlex reference match; not the full global list).
- 2025 Diophantine equations on cross-multiplicative forms of the Pell and Pell-Lucas numbersCitations 0 · OpenAlex
- 2025 Exploring Sums of Squares and Cubes of Fibonacci Numbers in Diophantine EquationsCitations 0 · OpenAlex
- 2025 Diophantine equations on cross-multiplicative forms of the Pell and Pell-Lucas numbersCitations 0 · OpenAlex