Results 1 to 10 of about 7,072 (130)

Linear forms in elliptic logarithms

Journal of Number Theory, 1985
The author studies lower bounds for linear forms in elliptic integrals in the case of complex multiplications, and related estimates for dependence relations of such numbers. His results considerably improves on the previous works of D. Masser and M. Anderson on these topics, the main feature being a sharp dependence on the heights of the corresponding
Kunrui Yu
exaly   +3 more sources

Matrices whose coefficients are linear forms in logarithms

Journal of Number Theory, 1992
Denote by \(L\) the \({\mathbb{Q}}\)-vector space of complex numbers \(\ell\) such that \(e^{\ell}\) is an algebraic number, and by \({\mathcal L}\) the vector space generated by \(1\) and \(L\) over the field \(\overline\mathbb{Q}\) of algebraic numbers.
Damien Roy
exaly   +2 more sources

Repdigits in the base $b$ as sums of four balancing numbers [PDF]

Mathematica Bohemica, 2021
The sequence of balancing numbers $(B_n)$ is defined by the recurrence relation $B_n=6B_{n-1}-B_{n-2}$ for $n\geq2$ with initial conditions $B_0=0$ and $B_1=1.$ $B_n$ is called the $n$th balancing number. In this paper, we find all repdigits in the base $
Refik Keskin, Fatih Erduvan
doaj   +1 more source

Curious Generalized Fibonacci Numbers

Mathematics, 2021
A generalization of the well-known Fibonacci sequence is the k−Fibonacci sequence whose first k terms are 0,…,0,1 and each term afterwards is the sum of the preceding k terms. In this paper, we find all k-Fibonacci numbers that are curious numbers (i.e.,
Jose L. Herrera, Jhon J. Bravo, Carlos A. Gómez   +2 more
doaj   +1 more source

Fermat $k$-Fibonacci and $k$-Lucas numbers [PDF]

Mathematica Bohemica, 2020
Using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and Pethő, we find all $k$-Fibonacci and $k$-Lucas numbers which are Fermat numbers.
Jhon J. Bravo, Jose L. Herrera
doaj   +1 more source

A kit for linear forms in three logarithms

Mathematics of Computation, 2023
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds for linear forms in logarithms.
Maurice Mignotte, Paul Voutier
openaire   +2 more sources

On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers

Karpatsʹkì Matematičnì Publìkacìï, 2021
The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
doaj   +1 more source

Fermat and Mersenne numbers in $k$-Pell sequence

Математичні Студії, 2021
For an integer $k\geq 2$, let $(P_n^{(k)})_{n\geq 2-k}$ be the $k$-generalized Pell sequence, which starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is defined by the recurrence $ P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}
B. Normenyo, S. Rihane, A. Togbe
doaj   +1 more source

A Quadratic Diophantine Equation Involving Generalized Fibonacci Numbers

Mathematics, 2020
The sequence of the k-generalized Fibonacci numbers ( F n ( k ) ) n is defined by the recurrence F n ( k ) = ∑ j = 1 k F n − j ( k ) beginning with the k terms 0 , … , 0 , 1 .
Ana Paula Chaves, Pavel Trojovský
doaj   +1 more source

First biometrics record of bartail flathead, Platycephalus indicus (Linnaeus, 1758) from the Bay of Bengal, Bangladesh

Heliyon, 2022
For the very first time the sex ratio, length-weight relationships (LWRs), length-length relationships (LLRs), form factor, as well as condition factor were calculated for bartail flathead, Platycephalus indicus, captured with gill nets (mesh size: 2.0–6.
Md. Rahamat Ullah, Md Mahamudul Hasan Mredul   +1 more
doaj   +1 more source