PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

The terms of the form $7kx^{2}$ in the generalized Lucas sequence with parameters $P$ and $Q$

Volume 173 / 2016

Olcay Karaatlı Acta Arithmetica 173 (2016), 81-95 MSC: 11B37, 11B39, 11B50. DOI: 10.4064/aa8247-2-2016 Published online: 14 April 2016

Abstract

Let $V_{n}(P,Q)$ denote the generalized Lucas sequence with parameters $P$ and $Q.$ For all odd relatively prime values of $P$ and $Q$ such that $P^{2}+4Q \gt 0,$ we determine all indices $n$ such that $V_{n}(P,Q)=7kx^{2}$ when $k\, |\, P.$ As an application, we determine all indices $n$ such that the equation $V_{n}=21x^{2}$ has solutions.

Authors

  • Olcay KaraatlıDepartment of Mathematics
    Faculty of Arts and Sciences
    Sakarya University
    54187 Sakarya, Turkey
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image