Let P and Q be nonzero integers. The generalized Fibonacci and Lucas sequences are defined respectively as follows: U₀ = 0, U₁ = 1, V₀ = 2, V₁ = P and , for n ≥ 1. In this paper, when w ∈ 1,2,3,6, for all odd relatively prime values of P and Q such that P ≥ 1 and P² + 4Q > 0, we determine all n and m satisfying the equation Uₙ = wUₘx². In particular, when k|P and k > 1, we solve the equations Uₙ = kx² and Uₙ = 2kx². As a result, we determine all n such that Uₙ = 6x².
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa8436-4-2016,
author = {Zafer \c Siar and Refik Keskin},
title = {On square classes in generalized Fibonacci sequences},
journal = {Acta Arithmetica},
volume = {172},
year = {2016},
pages = {277-295},
zbl = {06622304},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8436-4-2016}
}
Zafer Şiar; Refik Keskin. On square classes in generalized Fibonacci sequences. Acta Arithmetica, Tome 172 (2016) pp. 277-295. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8436-4-2016/