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)


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].


Modular Form Elliptic Curf Arithmetic Progression Diophantine Equation Consecutive Integer 
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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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