Herbert Batte

collaborators

10 papers

math.NT2026

On the Diophantine Inequality $∣ x^{2} - 2^{a} \cdot 3^{b} ∣ < 3 max {a, b}$

Banu Ä°rez AydÄ±n, Herbert Batte, Ä°lker Ä°nam +2

In this paper, we show that there are $57$ nonnegative integer solutions $(a, b, x)$ to the inequality $1 \leq ∣ x^{2} - 2^{a} \cdot 3^{b} ∣ < 3 max {a, b}$ and we list them e…

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

On mixed $b$ -concatenations of Fibonacci and Lucas numbers that are Lucas numbers

Herbert Batte, Prosper Kaggwa

Let $(F_{n})_{n \geq 0}$ and $(L_{n})_{n \geq 0}$ denote the sequences of Fibonacci and Lucas numbers respectively. This paper determines all Lucas numbers that can be represented as base $b…

math.NT2026

On Wagstaff primes in the $k$ -Lucas number sequence

Herbert Batte

A Wagstaff prime is a prime number of the form $(2^{p} + 1) /3$ , where $p$ is an odd prime. Let $(L_{n}^{(k)})_{n \geq 2 - k}$ be the $k$ -Lucas number sequence define…

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…

On the Diophantine Inequality ∣x2−2a⋅3b∣<3max{a,b}

Cullen and Woodall numbers in Padovan and Perrin sequences

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

On mixed b-concatenations of Fibonacci and Lucas numbers that are Lucas numbers

On Wagstaff primes in the k-Lucas number sequence

Product of powers of distinct primes as sums of Fibonacci numbers

On the Diophantine Inequality $∣ x^{2} - 2^{a} \cdot 3^{b} ∣ < 3 max {a, b}$

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

On mixed $b$ -concatenations of Fibonacci and Lucas numbers that are Lucas numbers

On Wagstaff primes in the $k$ -Lucas number sequence