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On the exponential local-global principle

Volume 159 / 2013

Boris Bartolome, Yuri Bilu, Florian Luca Acta Arithmetica 159 (2013), 101-111 MSC: Primary 11D61; Secondary 11J86, 11J87. DOI: 10.4064/aa159-2-1

Abstract

Skolem conjectured that the “power sum” ${A(n)=\lambda _1 \alpha _1^n + \cdots + \lambda _m \alpha _m^n}$ satisfies a certain local-global principle. We prove this conjecture in the case when the multiplicative group generated by ${\alpha _1, \ldots , \alpha _m}$ is of rank $1$.

Authors

  • Boris BartolomeEnteleia Tech
    La Cour
    31320 Auréville, France
    e-mail
  • Yuri BiluIMB, Université Bordeaux 1
    351 cours de la Libération
    33405 Talence France
    e-mail
  • Florian LucaFundación Marcos Moshinsky
    Circuito Exterior, C.U., Apdo. Postal 70-543
    Mexico D.F. 04510, México
    e-mail

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