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On binomial Thue-Mahler equations

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Abstract

We give a rather sharp upper bound for the degree of a binomial Thue--Mahler equation in terms of the coefficients and the primes involved. Further, we establish explicit lower bounds for the greatest prime factor of a binomial binary form at integral points. Our estimates considerably generalize and improve the earlier results obtained in this direction.

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Authors and Affiliations

  1. Université Louis Pasteur 7, rue René Descartes, 67084 Strasbourg, France

    Yann Bugeaud

  2. Number Theory Research Group of the Hungarian Academy of Sciences, Institute of Mathematics, University of Debrecen, 4010 Debrecen, P.O.B. 12, Hungary

    Kálmán Győry

Authors
  1. Yann Bugeaud
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  2. Kálmán Győry
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Bugeaud, Y., Győry, K. On binomial Thue-Mahler equations. Period Math Hung 49, 25–34 (2004). https://doi.org/10.1007/s10998-004-0520-0

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  • DOI: https://doi.org/10.1007/s10998-004-0520-0

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