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MAHADI DDAMULIRA
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Volume 127 Issue 3 June 2017 pp 411-421 Research Article
On a problem of Pillai with Fibonacci numbers and powers of 2
MAHADI DDAMULIRA FLORIAN LUCA MIHAJA RAKOTOMALALA
In this paper, we find all integers $c$ having at least two representations as a difference between a Fibonacci number and a power of 2.
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Volume 130 All articles Published: 23 September 2020 Article ID 0058 Article
The $x$-coordinates of Pell equations and sums of two Fibonacci numbers II
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.
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Proceedings – Mathematical Sciences
Volume 130, 2020
All articles
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