On the x--coordinates of Pell equations that are products of two Padovan numbers
Résumé
Let {Pn}n≥0 be the sequence of Padovan numbers defined by P0=0, P1=P2=1, and Pn+3=Pn+1+Pn for all n≥0. In this paper, we find all positive square-free integers d≥2 such that the Pell equations x2−dy2=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.
Domaines
Théorie des nombres [math.NT]Origine | Fichiers produits par l'(les) auteur(s) |
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