ON EXPRESSING TRIBONACCI NUMBERS AS PRODUCTS OF TWO PERRIN NUMBERS

ASES IX. INTERNATIONAL SCIENTIFIC RESEARCH CONGRESS , Adıyaman, Türkiye, 8 - 10 Mayıs 2025, ss.12-14, (Özet Bildiri)

involving classical number sequences such as the Fibonacci, Lucas, and Pell

sequences. These investigations—especially on equalities, factorization

identities, and exponential equations—have led to important developments in

both theoretical and computational number theory. Extending this exploration

to less-studied sequences opens new directions in the field.

In this paper, we investigate the circumstances under which a Tribonacci

number can be expressed as the product of two Perrin numbers. Specifically,

we examine all positive integer solutions of the Diophantine equation 𝑇􀯡 􀵌

𝑅􀯞. 𝑅􀯠. By effectively applying Baker's method based on linear forms in

logarithms, combined with precise analytic estimates and reduction

techniques, we show that there are exactly seven such solutions. Our findings

contribute to a deeper understanding of multiplicative relationships between

distinct linear recurrence sequences.

This talk is joint work with Ilker Inam (Bilecik), and Meltem Senadim

(Bilecik).