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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.

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