The $x$-coordinates of Pell equations and sums of two Fibonacci numbers II
Click here to view fulltext PDF
Permanent link:
https://www.ias.ac.in/article/fulltext/pmsc/130/0058
Let $\{Fn\}_{n≥0}$ be the sequence of Fibonacci numbers defined by $F_0 = 0$, $F_1 = 1$ and $F_{n+2} = F_{n+1}+F_n$ for all $n\geq 0$. In this paper, for an integer $d \geq 2$ which is square-free, we show that there is at most one value of the positive integer $x$ participating in the Pell equation $x^2 − dy^2 = \pm 4$ which is a sum of two Fibonacci numbers, with a few exceptions that we completely characterize.
MAHADI DDAMULIRA1 FLORIAN LUCA2 3 4
Volume 130, 2020
All articles
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode
© 2021-2022 Indian Academy of Sciences, Bengaluru.