Florian Luca
Articles written in Proceedings – Mathematical Sciences
Volume 116 Issue 1 February 2006 pp 1-8
Arithmetic properties of the Ramanujan function
Florian Luca Igor E Shparlinski
We study some arithmetic properties of the Ramanujan function τ(n), such as the largest prime divisor
Volume 124 Issue 2 May 2014 pp 141-154
Repdigits in 𝑘-Lucas Sequences
For an integer $k\geq 2$, let $(L_n^{(k)})_n$ be the 𝑘-Lucas sequence which starts with $0,\ldots,0,2,1$ (𝑘 terms) and each term afterwards is the sum of the 𝑘 preceding terms. In 2000, Luca (
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.
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.
Volume 131, 2021
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