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pro vyhledávání: '"Ddamulira, Mahadi"'
Let $ \{L_n\}_{n\geq 0} $ be the sequence of Lucas numbers. In this paper, we look at the exponential Diophantine equation $L_n-2^x3^y=c$, for $n,x,y\in \mathbb{Z}_{\ge0}$. We treat the cases $c\in -\mathbb{N}$, $c=0$ and $c\in \mathbb{N}$ independen
Externí odkaz:
http://arxiv.org/abs/2401.06555
Let $(N_{n})_{n\ge 0}$ be Narayana's cows sequence given by a recurrence relation $ N_{n+3}=N_{n+2}+N_n $ for all $ n\ge 0 $, with initial conditions $ N_0=0 $, and $ N_1= N_2=1 $. In this paper, we find all members in Narayana's cow sequence that ar
Externí odkaz:
http://arxiv.org/abs/2312.17571
Let $(L_n^{(k)})_{n\geq 2-k}$ be the sequence of $k$-generalized Lucas numbers for some fixed integer $k\ge 2$, whose first $k$ terms are $0,\;\ldots\;,\;0,\;2,\;1$ and each term afterward is the sum of the preceding $k$ terms. In this paper, we find
Externí odkaz:
http://arxiv.org/abs/2311.14001
Let $ (N_n)_{n\ge 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\ge 0 $. In this paper, we determine all Narayana numbers that are concatenations of two
Externí odkaz:
http://arxiv.org/abs/2210.00926
Publikováno v:
Glasnik Matematicki, 2022
Let $ \{F_n\}_{n\ge 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 $F_k-p^\ell$ with $k\ge 2$ and $\ell\ge 0$. We prove that $m_{F,p}(c)\
Externí odkaz:
http://arxiv.org/abs/2207.12868
Let $ (P_n)_{n\ge 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\ge 0 $. In this paper, we use Baker's theory for nonzero linear forms in logarithms of algebr
Externí odkaz:
http://arxiv.org/abs/2105.08515
Publikováno v:
Indagationes Mathematicae, 2021
Let $r\ge 1$ be an integer and ${\bf U}:=\{U_n\}_{n\ge 0}$ be the Lucas sequence given by $U_0=0,~U_1=1$, and $U_{n+2}=rU_{n+1}+U_n$ for $n\ge 0$. In this paper, we explain how to find all the solutions of the Diophantine equation, $AU_{n}+BU_{m}=CU_
Externí odkaz:
http://arxiv.org/abs/2105.01569
Publikováno v:
In Indagationes Mathematicae September 2024
Autor:
Ddamulira, Mahadi
Publikováno v:
Mathematica Slovaca,2020
Let $ (P_{n})_{n\ge 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\ge 0 $. In this paper, we find all Padovan numbers that are concatenations of two distinct repdigits.
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Externí odkaz:
http://arxiv.org/abs/2003.10705
Autor:
Ddamulira, Mahadi, Luca, Florian
Publikováno v:
The Ramanujan Journal, 2020
Let $r\ge 1$ be an integer and ${\bf U}:=(U_{n})_{n\ge 0} $ be the Lucas sequence given by $U_0=0$, $U_1=1, $ and $U_{n+2}=rU_{n+1}+U_n$, for all $ n\ge 0 $. In this paper, we show that there are no positive integers $r\ge 3,~x\ne 2,~n\ge 1$ such tha
Externí odkaz:
http://arxiv.org/abs/2001.10265