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On the length of arithmetic progressions in linear combinations of S-units

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An Erratum to this article was published on 26 October 2014

Abstract

Recent finiteness results concerning the lengths of arithmetic progressions in linear combinations of elements from finitely generated multiplicative groups have found applications to a variety of problems in number theory. In the present paper, we significantly refine the existing arguments and give an explicit upper bound on the length of such progressions.

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Authors and Affiliations

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

    Lajos Hajdu

  2. Mathematical Institute, UNAM, Ap. Postal 61-3 (Xangari), CP 58 089, Morelia, Michoacán, Mexico

    Florian Luca

Authors
  1. Lajos Hajdu
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  2. Florian Luca
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Correspondence to Lajos Hajdu.

Additional information

To Professors A. Pethő and J. Pintz on the occasion of their 60th birthdays

L. Hajdu was supported in part by the Hungarian Academy of Sciences and by the OTKA grants K67580 and K75566. F. Luca was supported in part by Grants SEP-CONACyT 79685 and PAPIIT 100508. Both authors were also supported in part by CONACyT and NKTH in the frame of the joint Mexican-Hungarian project “Diophantine equations and their applications in Cryptography”.

An erratum to this article is available at http://dx.doi.org/10.1007/s00013-014-0681-x.

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Hajdu, L., Luca, F. On the length of arithmetic progressions in linear combinations of S-units. Arch. Math. 94, 357–363 (2010). https://doi.org/10.1007/s00013-010-0111-7

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  • DOI: https://doi.org/10.1007/s00013-010-0111-7

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