The terms of the form 7kx² in the generalized Lucas sequence with parameters P and Q

• Autorzy: Olcay Karaatlı
• Języki publikacji: EN

Abstrakty

EN

Let Vₙ(P,Q) denote the generalized Lucas sequence with parameters P and Q. For all odd relatively prime values of P and Q such that P² + 4Q > 0, we determine all indices n such that Vₙ(P,Q) = 7kx² when k|P. As an application, we determine all indices n such that the equation Vₙ = 21x² has solutions.

Kategorie tematyczne

• 11B37: Recurrences
• 11B39: Fibonacci and Lucas numbers and polynomials and generalizations
• 11B50: Sequences (mod m )

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 173
• Numer: 1
• Strony: 81-95

Daty

wydano

2016

Twórcy

autor

Olcay Karaatlı

• Department of Mathematics, Faculty of Arts and Sciences, Sakarya University, 54187 Sakarya, Turkey

Identyfikatory

DOI

10.4064/aa8247-2-2016