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Pell-Type Equations

  • Titu Andreescu
  • Dorin Andrica
  • Ion Cucurezeanu
Chapter

Abstract

In 1909, A. Thue proved the following important theorem: Let f = a n z n +a n -1zn-1+…+a1z+a0 be an irreducible polynomial of degree ≥ 3 with integral coefficients. Consider the corresponding homogeneous polynomial
$$F(x,y)=y^nf\left(\frac{x}{y}\right)=a_nx^n+a_{n-1}x^{n-1}y+\cdots+a_1xy^{n-1}+a_0y^n.$$

Keywords

Positive Integer Fundamental Solution Integral Solution Diophantine Equation Great Common Divisor 
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

© Birkhäuser Boston 2009

Authors and Affiliations

  • Titu Andreescu
    • 1
  • 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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