S-integral solutions to a Weierstrass equation

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    Abstract

    The rational solutions with as denominators powers of 2 to the elliptic diophantine equation y2 = x3 - 228x + 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.
    Original languageEnglish
    Pages (from-to)281-301
    Number of pages21
    JournalJournal de Théorie des Nombres de Bordeaux
    Volume9
    Issue number2
    Publication statusPublished - 1997

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