Solving a specific Thue-Mahler equation

N. Tzanakis, B.M.M. de Weger

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    The diophantine equation x3 - 3xy2 - y3 = ± 3n017n119n2 is completely solved as follows. First, a large upper bound for the variables is obtained from the theory of linear forms in p-adic and real logarithms of algebraic numbers. Then this bound is reduced to a manageable size by p-adic and real computational diophantine approximation, based on the L3-algorithm. Finally the complete list of solutions is found in a sieving process. The method is in principle applicable to any Thue-Mahler equation, as the authors will show in a forthcoming paper.
    Original languageEnglish
    Pages (from-to)799-815
    Number of pages17
    JournalMathematics of computation
    Issue number57
    Publication statusPublished - 1991

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