TY - JOUR
AU - Şi̇ar, Zafer
AU - Keski̇n, Refi̇k
PY - 2016/03/07
Y2 - 2024/07/13
TI - The Square Terms in Generalized Lucas Sequence with Parameters $P$ And $Q$
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 118
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-23292
UR - https://www.mscand.dk/article/view/23292
SP - 13-26
AB - 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.
ER -