Diophantine equations for additive Pell numbers in Pell, Pell–Lucas, and Modified Pell numbers
Yazarlar (2)
Ahmet Emin Karabük Üniversitesi, Türkiye
Doç. Dr. Ahmet DAŞDEMİR Kastamonu Üniversitesi, Türkiye
| Makale Türü | Özgün Makale (ESCI dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | ||
| Dergi ISSN | 1310-5132 Wos Dergi | ||
| Dergi Tarandığı Indeksler | ESCI | ||
| Makale Dili | Türkçe | Basım Tarihi | 01-2026 |
| Cilt / Sayı / Sayfa | 32 / 1 / 112–119 | DOI | 10.7546/nntdm.2026.32.1.112-119 |
| Makale Linki | https://doi.org/10.7546/nntdm.2026.32.1.112-119 | ||
| UAK Araştırma Alanları |
Cebir ve Sayılar Teorisi
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| Özet |
| This paper investigates the Diophantine equations arising from ternary additive problems of Pell, Pell–Lucas, and Modified Pell numbers. Specifically, we characterize all integer solutions to the equation Pn+ Pm+ Pr= Xk, X∈{P, Q, R}, where Pi, Qi, and Ri denote the i-th terms of the Pell, Pell–Lucas, and Modified Pell sequences, respectively. By leveraging recurrence relations, Binet’s formulas, and Carmichael’s Primitive Divisor Theorem, we provide the first complete classification of solutions to this ternary additive problem. Our results reveal several parametric and singular solutions. Furthermore, we reduce prior results to binary sums of the form Pn+ Pm= Xk as special instances of our framework. |
| Anahtar Kelimeler |
| Pell number | Pell-Lucas number | Primitive divisor | Diophantine equation | Binet's formula |
| Atıf Sayıları | |
| Web of Science | 1 |
| Google Scholar | 1 |