Florian Luca

activity

20242026

collaborators

6 papers

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 StÄnicÄ

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…

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

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