M. Ddamulira

activity

20172025

most citedOn a problem of Pillai with Fibonacci numbers and powers of 2

33 citations · 58 across the 17 of their papers we have counts for

collaborators

19 papers

math.NT2025

On concatenations of two $k$ -generalized Lucas numbers

Alex Behakanira Tumwesigye, Mahadi Ddamulira, Prosper Kaggwa

For an integer $ k \geq 2 $, the sequence of $ k $-generalized Lucas numbers is defined by the recurrence relation $ L_n^{(k)} = L_{n-1}^{(k)} + \cdots + L_{n-k}^{(k)} $ for…

math.NT2025

Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits

Mahadi Ddamulira

The Tribonacci-Lucas sequence ${S_{n}}_{n \geq 0}$ is defined by the linear recurrence relation $S_{n + 3} = S_{n + 2} + S_{n + 1} + S_{n}$ , for $n \geq 0$ , with the initial conditions $S_0…

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.NT2023

Palindromic concatenations of two distinct repdigits in Narayana's cows sequence

Mahadi Ddamulira, Paul Emong, Geoffrey Ismail Mirumbe

Let $(N_{n})_{n \geq 0}$ be Narayana's cows sequence given by a recurrence relation $N_{n + 3} = N_{n + 2} + N_{n}$ for all $n \geq 0$ , with initial conditions $N_{0} = 0$ , and $N_{1} = N_{2} = 1$ .…

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.NT2022★ 1 cited

Members of Narayana's cow sequence that are concatenations of two repdigits

Mahadi Ddamulira, Paul Emong, Geoffrey Ismail Mirumbe

Let $(N_{n})_{n \geq 0}$ be the Narayana's cow sequence defined by a third-order recurrence relation $N_{0} = 0, N_{1} = N_{2} = 1$ , and $N_{n + 3} = N_{n + 2} + N_{n}$ for all $n \geq 0$ . In this pa…

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,…

math.NT2021★ 1 cited

On the Shorey-Tijdeman Diophantine equation involving terms of Lucas sequences

Mahadi Ddamulira, Florian Luca, Robert Tichy

Let $r \geq 1$ be an integer and $U := {U_{n}}_{n \geq 0}$ be the Lucas sequence given by $U_{0} = 0, U_{1} = 1$ , and $U_{n + 2} = r U_{n + 1} + U_{n}$ for $n \geq 0$ . In this paper, we explain how to…

math.NT2020

Padovan numbers that are concatenations of two distinct repdigits

Mahadi Ddamulira

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

math.NT2020★ 4 cited

On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences

Mahadi Ddamulira, Florian Luca

Let $r \geq 1$ be an integer and $U := (U_{n})_{n \geq 0}$ be the Lucas sequence given by $U_{0} = 0$ , $U_{1} = 1,$ and $U_{n + 2} = r U_{n + 1} + U_{n}$ , for all $n \geq 0$ . In this paper, we show…

math.NT2019

Repdigits as sums of three Padovan numbers

Mahadi Ddamulira

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

math.NT2019

On the $x$ --coordinates of Pell equations which are products of two: Lucas numbers, Pell numbers

Mahadi Ddamulira

Let ${L_{n}}_{n \geq 0}$ be the sequence of Lucas numbers given by $L_{0} = 2, L_{1} = 1$ and $L_{n + 2} = L_{n + 1} + L_{n}$ for all $n \geq 0$ . In the first paper, for an integer $d \geq 2$ w…

math.NT2019★ 1 cited

On the $x -$ coordinates of Pell equations which are sums of two Padovan numbers

Mahadi Ddamulira

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

math.NT2019★ 15 cited

On the problem of Pillai with $k$ --generalized Fibonacci numbers and powers of $3$

Mahadi Ddamulira, Florian Luca

For an integer $k \geq 2$ , let ${F_{n}^{(k)}}_{n \geq 2 - k}$ be the $k$ --generalized Fibonacci sequence which starts with $0, \dots, 0, 1$ (a total of $k$ terms) and for which each t…

math.NT2019

On the problem of Pillai with Fibonacci numbers, Padovan numbers, and Tribonacci numbers and powers of $3$

Mahadi Ddamulira

Consider the sequences: ${F_{n}}_{n \geq 0}$ of Fibonacci numbers defined by $F_{0} = 0$ , $F_{1} = 1$ and $F_{n + 2} = F_{n + 1} + F_{n}$ for all $n \geq 0$ ; ${P_{n}}_{n \geq 0}$ of…

math.NT2018

On the $x$ --coordinates of Pell equations which are $k$ --generalized Fibonacci numbers

Mahadi Ddamulira, Florian Luca

For an integer $k \geq 2$ , let ${F_{n}^{(k)}}_{n ⩾ 2 - k}$ be the $k$ --generalized Fibonacci sequence which starts with $0, \dots, 0, 1$ (a total of $k$ terms) and for which…

math.NT2017★ 33 cited

On a problem of Pillai with Fibonacci numbers and powers of 2

Mahadi Ddamulira, Florian Luca, Mihaja Rakotomalala

In this paper, we find all integers c having at least two representations as a difference between a Fibonacci number and a power of 2.

math.NT2017★ 2 cited

Fibonacci Numbers which are Products of two Pell Numbers

Mahadi Ddamulira, Florian Luca, Mihaja Rakotomalala

In this paper, we find all Fibonacci numbers which are products of two Pell numbers and all Pell numbers which are products of two Fibonacci numbers.

On concatenations of two k-generalized Lucas numbers

Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits

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

Palindromic concatenations of two distinct repdigits in Narayana's cows sequence

Multiplicative independence in the sequence of k-generalized Lucas numbers

Members of Narayana's cow sequence that are concatenations of two repdigits

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

On the Shorey-Tijdeman Diophantine equation involving terms of Lucas sequences

Padovan numbers that are concatenations of two distinct repdigits

On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences

Repdigits as sums of three Padovan numbers

On the x--coordinates of Pell equations which are products of two: Lucas numbers, Pell numbers

On the x−coordinates of Pell equations which are sums of two Padovan numbers

On the problem of Pillai with k--generalized Fibonacci numbers and powers of 3

On the problem of Pillai with Fibonacci numbers, Padovan numbers, and Tribonacci numbers and powers of 3

On the x--coordinates of Pell equations which are k--generalized Fibonacci numbers

On a problem of Pillai with Fibonacci numbers and powers of 2

Fibonacci Numbers which are Products of two Pell Numbers

On concatenations of two $k$ -generalized Lucas numbers

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

On the $x$ --coordinates of Pell equations which are products of two: Lucas numbers, Pell numbers

On the $x -$ coordinates of Pell equations which are sums of two Padovan numbers

On the problem of Pillai with $k$ --generalized Fibonacci numbers and powers of $3$

On the problem of Pillai with Fibonacci numbers, Padovan numbers, and Tribonacci numbers and powers of $3$

On the $x$ --coordinates of Pell equations which are $k$ --generalized Fibonacci numbers