On Tribonacci numbers written as a product of two Perrin numbers

Demirkol Özkaya Z., İNAM İ., Senadim M.

Asian-European Journal of Mathematics, vol.18, no.11, 2025 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 11
  • Publication Date: 2025
  • Doi Number: 10.1142/s1793557125500512
  • Journal Name: Asian-European Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: applications of Baker’s method, Diophantine equations, Perrin numbers, Tribonacci numbers
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

In this paper, we give all solutions of the Diophantine equation Tn = RkRm, where (n, k, m) ∈ 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 effectively used for the solutions of different Diophantine equations involving classical number sequences such as Fibonacci or Lucas sequences.