@article{Şi̇ar_Keski̇n_2016, title={The Square Terms in Generalized Lucas Sequence with Parameters $P$ And $Q$}, volume={118}, url={https://www.mscand.dk/article/view/23292}, DOI={10.7146/math.scand.a-23292}, abstractNote={Let $P$ and $Q$ be nonzero integers. Generalized Lucas sequence is defined as follows: $V_{0}=2$, $V_{1}=P$, and $V_{n+1}=PV_{n}+QV_{n-1}$ for $n\geq 1$. We assume that $P$ and $Q$ are odd relatively prime integers. Firstly, we determine all indices $n$ such that $V_{n}=kx^{2}$ and $V_{n}=2kx^{2}$ when $k|P$. Then, as an application of our these results, we find all solutions of the equations $V_{n}=3x^{2}$ and $V_{n}=6x^{2}$. Moreover, we find integer solutions of some Diophantine equations. }, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Şi̇ar Zafer and Keski̇n Refi̇k}, year={2016}, month={Mar.}, pages={13–26} }