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Your search keyword '"Diophantine Equations"' showing total 2 results
Start Over Descriptor "Diophantine Equations" Region davenport (iowa)
2 results on '"Diophantine Equations"'

1. On the equation (2k - 1)(3l - 1) = 5m - 1.

Author

Luca, F. and Szalay, L.

Subjects
*ALGEBRAIC numbers, *DIOPHANTINE equations, *MODULAR arithmetic, *ALGORITHMS, *EQUATIONS, *MAPLE
Abstract

In this paper, we solve completely the title diophantine equation. The main tools are linear forms of logarithm of algebraic numbers, reduction methods, modular arithmetic. We use Maple to carry out some calculations corresponding to the LLL algorithm, Baker-Davenport reduction, and certain approximations. [ABSTRACT FROM AUTHOR]

Published
2020

2. Fibonacci Numbers with a Prescribed Block of Digits.

Author

Trojovský, Pavel

Subjects
*ALGEBRAIC numbers, *DIOPHANTINE approximation, *DIOPHANTINE equations, *LOGARITHMS, *REAL numbers
Abstract

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 Diophantine approximation. [ABSTRACT FROM AUTHOR]

Published
2020
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