On Tribonacci numbers written as a product of two Perrin numbers

Ozkaya Z. D., INAM I., Senadim M.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.1, no.1, pp.1-23, 2025 (ESCI)

  • Publication Type: Article / Article
  • Volume: 1 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1142/s1793557125500512
  • Journal Name: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.1-23
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, we give all solutions of the Diophantine equation Tn = RkRm, where

(n; k;m) 2 Z+ x Z+ x Z+, Rk is the Perrin sequence, and Tn is the Tribonacci sequence.

We show that this Diophantine equation has only 7 integer solution triples. For the

proof, we use Baker's method. Our motivation is to show that linear forms in logarithms

can still be e ectively used for the solutions of di erent Diophantine equations involving

beside classical number sequences such as Fibonacci or Lucas sequences.