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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa8247-2-2016,
author = {Olcay Karaatl\i },
title = {The terms of the form 7kx$^2$ in the generalized Lucas sequence with parameters P and Q},
journal = {Acta Arithmetica},
volume = {172},
year = {2016},
pages = {81-95},
zbl = {06574973},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8247-2-2016}
}
Olcay Karaatlı. The terms of the form 7kx² in the generalized Lucas sequence with parameters P and Q. Acta Arithmetica, Tome 172 (2016) pp. 81-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8247-2-2016/