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Currently displaying 1 – 3 of 3

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$S$ -integral solutions to a Weierstrass equation

Benjamin M. M. de Weger — 1997

Journal de théorie des nombres de Bordeaux

The rational solutions with as denominators powers of $2$ to the elliptic diophantine equation $y^{2} = x^{3} - 228 x + 848$ are determined. An idea of Yuri Bilu is applied, which avoids Thue and Thue-Mahler equations, and deduces four-term ( $S$ -) unit equations with special properties, that are solved by linear forms in real and $p$ -adic logarithms.

Padua and Pisa are exponentially far apart.

Benjamin M. M. De Weger — 1997

Publicacions Matemàtiques

We answer the question posed by Ian Stewart which Padovan numbers are at the same time Fibonacci numbers. We give a result on the difference between Padovan and Fibonacci numbers, and on the growth of Padovan numbers with negative indices.

Solving elliptic diophantine equations: the general cubic case

Roelof J. Stroeker; Benjamin M. M. de Weger — 1999

Acta Arithmetica

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