On Tribonacci numbers written as a product of three Fibonacci numbers
Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, cilt.34, sa.1, ss.117-128, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 34 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.2478/auom-2026-0006
- Dergi Adı: Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
- Sayfa Sayıları: ss.117-128
- Anahtar Kelimeler: applications of the Baker's method, Diophantine equations, Fibonacci numbers, linear forms in logarithms, Tribonacci numbers
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
The present paper examines the following Diophantine equation: Tn = Fk · Fl · Fm where Tn is the n-th Tribonacci number and likewise Fk is the k-th Fibonacci number and so on as variables. As an application of the Baker's method, we show that the equation has only one solution apart from the trivial one, namely (n, k, l, m) = (12, 4, 6, 8). This paper can be considered as a continuation work of the paper by Luca et al, 2023.