Herbert Batte

activity

20212026

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

1 citations · 2 across the 19 of their papers we have counts for

collaborators

21 papers

math.NT2026

$k$ -Fibonacci and $k$ -Lucas numbers with the Hölder inequality

Herbert Batte, Prosper Kaggwa

Dujella, Jak\v setić and Pe\v carić recently established in \cite{DJP}, a chain of power-sum inequalities, built from Hölder's and Cauchy's inequalities and their converse forms, a…

math.NT2026

$k$ -Lucas Annulus for Polynomial Zeros

Herbert Batte

We prove a binomial identity relating the $k$ -Lucas and $k$ -Fibonacci sequences: for real $k > 0$ and integers $m \geq 1$ , $n \geq 1$ , a binomial-weighted sum of $k$ -Lucas numbers reduces…

math.NT2026

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

Banu İrez Aydın, Herbert Batte, İlker İnam +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 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

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…

math.GM2025

On Palindromic forms in the $k$ -Lucas sequence composed of two distinct Repdigits

Herbert Batte, Prosper Kaggwa

For integers $k \geq 2$ , the $k$ -generalized Lucas sequence ${L_{n}^{(k)}}_{n \geq 2 - k}$ is defined by the recurrence relation \[ L_n^{(k)} = L_{n-1}^{(k)} + \cdots + L_{n-k}^{(k)}…

math.NT2025

On the Largest Prime factor of the $k$ -generalized Pell numbers

Herbert Batte

Let $k \geq 2$ be an integer and consider the $k$ -generalized Pell sequence ${P_{n}^{(k)}}_{n \geq 2 - k}$ , defined by the initial values $0, \dots, 0, 0, 1$ (a total of $k$ terms), a…

math.NT2025

On $k$ -Pell numbers that are Palindromes formed by two distinct Repdigits

Herbert Batte, Darius Guma

Let $k \geq 2$ and consider the sequence ${P_{n}^{(k)}}_{n \geq 2 - k}$ of $k$ -generalized Pell numbers, which begins with the first $k$ terms as $0, \dots, 0, 0, 1$ , and satisfies th…

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.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

Perrin numbers that are palindromic concatenations of two repdigits

Herbert Batte, Prosper Kaggwa

Let ${P_{n}}_{n \geq 0}$ be the sequence of Perrin numbers defined by $P_{0} = 3$ , $P_{1} = 0$ , $P_{2} = 2$ and $P_{n + 3} = P_{n + 1} + P_{n}$ for all $n \geq 0$ . In this paper, we determine all Perr…

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.GM2023

Lucas numbers that are palindromic concatenations of two distinct repdigits

Herbert Batte

Let ${L_{n}}_{n \geq 0}$ be the sequence of Lucas numbers. In this paper, we determine all Lucas numbers that are palindromic concatenations of two distinct repdigits.

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.NT2022★ 1 cited

On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime

Herbert Batte, Mahadi Ddamulira, Juma Kasozi +1

Let ${F_{n}}_{n \geq 0}$ be the sequence of Fibonacci numbers and let $p$ be a prime. For an integer $c$ we write $m_{F, p} (c)$ for the number of distinct representations of $c$ as…

math.NT2021

Perrin numbers that are concatenations of two distinct repdigits

Herbert Batte, Taboka P. Chalebgwa, Mahadi Ddamulira

Let $(P_{n})_{n \geq 0}$ be the sequence of Perrin numbers defined by ternary relation $P_{0} = 3$ , $P_{1} = 0$ , $P_{2} = 2$ , and $P_{n + 3} = P_{n + 1} + P_{n}$ for all $n \geq 0$ . In this paper,…

k-Fibonacci and k-Lucas numbers with the Hölder inequality

k-Lucas Annulus for Polynomial Zeros

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 Palindromic forms in the k-Lucas sequence composed of two distinct Repdigits

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

On k-Pell numbers that are Palindromes formed by two distinct Repdigits

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

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

Perrin numbers that are palindromic concatenations of two repdigits

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

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

Lucas numbers that are palindromic concatenations of two distinct repdigits

Multiplicative independence in the sequence of k-generalized Lucas numbers

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

On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime

Perrin numbers that are concatenations of two distinct repdigits

$k$ -Fibonacci and $k$ -Lucas numbers with the Hölder inequality

$k$ -Lucas Annulus for Polynomial Zeros

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

On Palindromic forms in the $k$ -Lucas sequence composed of two distinct Repdigits

On the Largest Prime factor of the $k$ -generalized Pell numbers

On $k$ -Pell numbers that are Palindromes formed by two distinct Repdigits

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

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

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