Florian Luca

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20112026

most citedOn the Largest Prime factor of the k-generalized Lucas numbers

1 citations · 1 across the 13 of their papers we have counts for

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math.NT2026

Cullen and Woodall numbers in Padovan and Perrin sequences

Herbert Batte, Eric F. Bravo, Florian Luca

Let ${P_{n}}_{n \geq 0}$ and ${R_{n}}_{n \geq 0}$ denote the Padovan and Perrin sequences, both satisfying the recurrence $U_{n + 3} = U_{n + 1} + U_{n}$ , but with initial values $P_0 = P_1…

math.NT2026

On generalized Thabit numbers $(p + 1) p^{a} - 1$ in the $k$ -Lucas sequence

Herbert Batte, Florian Luca, Pantelimon Stănică

Let $k \geq 2$ and ${L_{n}^{(k)}}_{n \geq 2 - k}$ be the sequence of $k$ -Lucas numbers whose first $k$ terms are $0, \dots, 0, 2, 1$ and each term afterwards is the sum of the preceding $k…

math.NT2026

Product of powers of distinct primes as sums of Fibonacci numbers

Herbert Batte, Florian Luca, Volker Ziegler

Let $F_{n}$ be the $n$ -th Fibonacci number. In this paper, we study the Diophantine equation $F_{n} + F_{m} = p^{x} q^{y}$ in nonnegative integers $n \geq m$ , $x$ and $y$ , where $p$ and $q$ are fix…

math.NT2025

$k$ -Fibonacci numbers that are palindromic concatenations of two distinct Repdigits

Herbert Batte, Florian Luca

Let $k \geq 2$ and ${F_{n}^{(k)}}_{n \geq 2 - k}$ be the sequence of $k$ --generalized Fibonacci numbers whose first $k$ terms are $0, \dots, 0, 0, 1$ and each term afterwards is the sum of…

math.NT2025

The Discriminant of the Characteristic Polynomial of the $k$ th Fibonacci sequence is not a member of the $k$ th Lucas sequence

Herbert Batte, Florian Luca

Let $k \geq 2$ and ${L_{n}^{(k)}}_{n \geq 2 - k}$ be the sequence of $k$ -generalized Lucas numbers whose first $k$ terms are $0, \dots, 0, 2, 1$ and each term afterwards is the sum of the…

math.NT2024

On a nonlinear Diophantine equation with powers of three consecutive $k$ --Lucas Numbers

Herbert Batte, Florian Luca

Let $(L_{n}^{(k)})_{n \geq 2 - k}$ be the sequence of $k$ --generalized Lucas numbers for some fixed integer $k \geq 2$ whose first $k$ terms are $0, \dots, 0, 2, 1$ and each term afterwards…

math.NT2024

Solutions to a Pillai-type equation involving Tribonacci numbers and S-units

Herbert Batte, Florian Luca

Let ${T_{n}}_{n \geq 0}$ be the sequence of Tribonacci numbers. In this paper, we study the exponential Diophantine equation $T_{n} - 2^{x} 3^{y} = c$ , for $n, x, y \in Z_{\geq 0}$ . In p…

math.NT2024

On a problem of Pillai involving S-units and Lucas numbers

Herbert Batte, Mahadi Ddamulira, Juma Kasozi +1

Let ${L_{n}}_{n \geq 0}$ be the sequence of Lucas numbers. In this paper, we look at the exponential Diophantine equation $L_{n} - 2^{x} 3^{y} = c$ , for $n, x, y \in Z_{\geq 0}$ . We trea…

math.NT2023

Multiplicative independence in the sequence of $k$ -generalized Lucas numbers

Herbert Batte, Mahadi Ddamulira, Juma Kasozi +1

Let $(L_{n}^{(k)})_{n \geq 2 - k}$ be the sequence of $k$ -generalized Lucas numbers for some fixed integer $k \geq 2$ , whose first $k$ terms are $0, \dots, 0, 2, 1$ and each term a…

math.NT2023★ 1 cited

On the Largest Prime factor of the k-generalized Lucas numbers

Herbert Batte, Florian Luca

Let $(L_{n}^{(k)})_{n \geq 2 - k}$ be the sequence of $k$ --generalized Lucas numbers for some fixed integer $k \geq 2$ whose first $k$ terms are $0, \dots, 0, 2, 1$ and each term afterwards…

math.NT2023

On the discriminator of Lucas sequences. II

Matteo Ferrari, Florian Luca, Pieter Moree

The family of Shallit sequences consists of the Lucas sequences satisfying the recurrence $U_{n + 2} (k) = (4 k + 2) U_{n + 1} (k) - U_{n} (k),$ with initial values $U_{0} (k) = 0$ and $U_{1} (k) = 1$ and w…

math.NT2023

Sequences of integers generated by two fixed primes

Alessandro Languasco, Florian Luca, Pieter Moree +1

Let $p$ and $q$ be two distinct fixed prime numbers and $(n_{i})_{i \geq 0}$ the sequence of consecutive integers of the form $p^{a} \cdot q^{b}$ with $a, b \geq 0$ . Tijdeman gave a lower bou…

math.NT2011

Values of the Euler phi-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields

Kevin Ford, Florian Luca, Pieter Moree

For a fixed odd prime q we investigate the first and second order terms of the asymptotic series expansion for the number of n\le x such that q does not divide phi(n). Part of the…

Cullen and Woodall numbers in Padovan and Perrin sequences

On generalized Thabit numbers (p+1)pa−1 in the k-Lucas sequence

Product of powers of distinct primes as sums of Fibonacci numbers

k-Fibonacci numbers that are palindromic concatenations of two distinct Repdigits

The Discriminant of the Characteristic Polynomial of the kth Fibonacci sequence is not a member of the kth Lucas sequence

On a nonlinear Diophantine equation with powers of three consecutive k--Lucas Numbers

Solutions to a Pillai-type equation involving Tribonacci numbers and S-units

On a problem of Pillai involving S-units and Lucas numbers

Multiplicative independence in the sequence of k-generalized Lucas numbers

On the Largest Prime factor of the k-generalized Lucas numbers

On the discriminator of Lucas sequences. II

Sequences of integers generated by two fixed primes

Values of the Euler phi-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields

On generalized Thabit numbers $(p + 1) p^{a} - 1$ in the $k$ -Lucas sequence

$k$ -Fibonacci numbers that are palindromic concatenations of two distinct Repdigits

The Discriminant of the Characteristic Polynomial of the $k$ th Fibonacci sequence is not a member of the $k$ th Lucas sequence

On a nonlinear Diophantine equation with powers of three consecutive $k$ --Lucas Numbers

Multiplicative independence in the sequence of $k$ -generalized Lucas numbers