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Some Advanced Methods for Solving Diophantine Equations

  • Titu Andreescu
  • Dorin Andrica
  • Ion Cucurezeanu
Chapter

Abstract

A field is a set k equipped with two commutative binary operations, addition and multiplication, such that
  • (k, +) is an abelian group under addition;

  • every nonzero element of k has a multiplicative inverse, and (k*, ·) is an abelian group under multiplication, where k* = k \ {0k};

  • 0k ≠ 1k;

  • the distributive law holds: (a + b)c = ac + bc for all a, b, c Є k.

Keywords

Prime Divisor Diophantine Equation Quadratic Residue Nonzero Integer Multiplicative Inverse 
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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