Work

On Tribonacci numbers written as a product of two Perrin numbers

Year: 2025

Type: article

Abstract: In this paper, we give all solutions of the Diophantine equation [Formula: see text], where [Formula: see text] x [Formula: see text] x [Formula: see text], [Formula: see text] is the Perrin sequence, and [Formula: see text] is the Tribonacci sequence. We show that this Diophantine equation has only [Formula: see text] integer solution triples. For the proof, we use Baker’s method. Our motivation is to show that linear forms in logarithms can still be effectively used for the solutions of different Diophantine equations involving classical number sequences such as Fibonacci or Lucas sequences.

Source: Asian-European Journal of Mathematics

DOI: 10.1142/s1793557125500512

Authors: Zeynep Demirkol Ozkaya, Ilker Inam, Meltem Senadim

Institutions: Van Yüzüncü Yıl Üniversitesi, Bilecik Şeyh Edebali Üniversitesi

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4409790428

FWCI:

Cites: 6

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Related to: 10