Some Advanced Methods for Solving Diophantine Equations



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.


Prime Divisor Diophantine Equation Quadratic Residue Nonzero Integer Multiplicative Inverse 


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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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