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…

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

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