Abstract
Let (P n) n≥0 be the sequence of Padovan numbers defined by P 0 = 0, P 1 = P 2 = 1, and P n+3 = P n+1 + P n for all n ≥ 0. In this paper, we find all positive square-free integers d ≥ 2 such that the Pell equations x 2 − dy 2 = ℓ, where ℓ ∈ {±1, ±4}, have at least two positive integer solutions (x, y) and (x ′, y ′) such that each of x and x ′ is a product of two Padovan numbers.
Originalsprache | englisch |
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Aufsatznummer | A70 |
Seiten (von - bis) | 1-20 |
Seitenumfang | 20 |
Fachzeitschrift | INTEGERS: Electronic Journal of Combinatorial Number Theory |
Jahrgang | 20 |
Publikationsstatus | Veröffentlicht - 31 Aug. 2020 |
ASJC Scopus subject areas
- Algebra und Zahlentheorie
Fields of Expertise
- Information, Communication & Computing