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Solutions to Pell-Type Equations

  • Titu AndreescuEmail author
  • Dorin Andrica
  • Ion Cucurezeanu
Chapter
  • 1.7k Downloads

Abstract

1. Find all positive integers n such that \(\frac{{n}({n+1})}{3}\)is a perfect square. (Dorin Andrica) Soloution. Let \(\frac{{n}({n+1})}{3} = y^2,\) which is equivalent to
$${(2n + 1)}^2 - 12y^2 = 1.$$

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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  • Titu Andreescu
    • 1
    Email author
  • Dorin Andrica
    • 2
    • 3
  • Ion Cucurezeanu
    • 4
  1. 1.School of Natural Sciences and MathematicsUniversity of Texas at DallasRichardsonUSA
  2. 2.Faculty of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania
  3. 3.Department of Mathematics College of ScienceKing Saud UniversityRiyadhSaudi Arabia
  4. 4.Faculty of Mathematics and Computer ScienceOvidius University of ConstantaConstantaRomania

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