Herbert Batte

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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

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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…

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

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