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Perfect Powers in Products with Consecutive Terms from Arithmetic Progressions, II

  • Kálmán Győry
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 25)

Abstract

There is a very rich literature on perfect powers or almost perfect powers in products of the form m(m + d) …: (m + (k − 1)d), where m, d are coprime positive integers and k ≥ 3. By a conjecture, such a product is never a perfect n-th power if k > 3, n ≥2 or k = 3, n > 2. In the classical case d = 1 the conjecture has been proved by Erdős and Selfridge [11]. The general case d ≥ 1 seems to be very hard, then there are only partial results; for survey papers on results obtained before 2006 we refer to Tijdeman [46]– [48], Shorey and Tijdeman [43, 44], Shorey [38]–[42]_and Győry [15, 16].

Keywords

Modular Form Elliptic Curf Arithmetic Progression Diophantine Equation Consecutive Integer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag 2013

Authors and Affiliations

  • Kálmán Győry
    • 1
  1. 1.Institute of MathematicsUniversity of DebrecenDebrecenHungary

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