Abstract
Let $P\geq 3$ be an integer. Let $(V_{n})$ denote generalized Lucas sequence defined by $V_{0}=2$, $V_{1}=P$, and $V_{n+1}=PV_{n}-V_{n-1}$ for $n\geq 1$. In this study, when $P$ is odd, we solve the equation $V_{n}=wx^{2}$ for some values of $w$. Moreover, when $P$ is odd, we solve the equation $V_{n}=wkx^{2}$ with $k \mid P$ and $k \gt 1$ for $w=3,11,13$. Lastly, we solve the equation $V_{n}=wV_{m}x^{2}$ for $w=7,11,13$.
Citation
Merve GÜNEY DUMAN. Ümmügülsüm ÖĞÜT. Refik KESKİN. "Generalized Lucas Numbers of the form $wx^{2}$ and $wV_{m}x^{2}$." Hokkaido Math. J. 47 (3) 465 - 480, October 2018. https://doi.org/10.14492/hokmj/1537948825
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