Results 11 to 20 of about 114,855,941 (268)

A p-adic lower bound for a linear form in logarithms [PDF]

International Journal of Number Theory, 2022
Linear forms in logarithms have an important role in the theory of Diophantine equations. In this paper, we prove explicit [Formula: see text]-adic lower bounds for linear forms in [Formula: see text]-adic logarithms of rational numbers using Padé approximations of the second kind.
Seppälä Louna, Palojärvi Neea
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Linear forms in two logarithms and interpolation determinants [PDF]

Acta Arithmetica, 1994
The author provides a precise lower bound for the absolute value of a linear combination of two logarithms of real algebraic numbers with integer coefficients. This lower bound is explicit and improves in the real case an earlier result of \textit{M. Mignotte} and \textit{M. Waldschmidt} [Ann. Fac. Sci. Toulouse Math.
Laurent, Michel
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Linear forms in logarithms and exponential Diophantine equations [PDF]

Hardy-Ramanujan Journal, 2020
This paper aims to show two things. Firstly the importance of Alan Baker's work on linear forms in logarithms for the development of the theory of exponential Diophantine equations. Secondly how this theory is the culmination of a series of greater and smaller discoveries.
Rob Tijdeman, Tijdeman, Rob
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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
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PRECIPITATION OF METAL HYDROXIDES FROM AQUEOUS SOLUTIONS AS A RESULT OF SPONTANEOUS CONDENSATION OF POLYNUCLEAR HYDROXOCOMPLEXES

KPI Science News, 2021
Background. Generally, it is assumed that the formation of a solid phase (precipitate) happens when the activities of the involved ions would exceed those defined by the thermodynamic solubility product.
Yuriy Andriyko, Aleksandr O. Andriiko
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About One Variational Problem, Leading to а Biharmonic Equation, and about the Approximate Solution of the Main Boundary Value Problem for this Equation

Наука и техника, 2022
. Many important questions in the theory of elasticity lead to a variational problem associated with a biharmonic equation and to the corresponding boundary value problems for such an equation.
I. N. Meleshko, P. G. Lasy
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Products of Factorials in Smarandache Type Expressions [PDF]

, 1997
The proof of Theorem 1 uses lower bounds for linear forms in logarithms of algebraiC numbers (see [1] and [7]) as well as an idea of Stewart (see [10])
Luca, Florian
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Fibonacci Numbers with a Prescribed Block of Digits

Mathematics, 2020
In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms of algebraic numbers and some tools from ...
Pavel Trojovský
doaj   +1 more source