Diophantine Equations

  • Kenneth Ireland
  • Michael Rosen
Part of the Graduate Texts in Mathematics book series (GTM, volume 84)


In Chapter10 we discussed Diophantine equations over finitefields. In this chapter we consider special Diophantine equations with integral coefficients and seek integral or rational solutions. The techniques used vary from elementary congruence considerations to the use of more sophisticated results in algebraic number theory. In addition to establishing the existence or nonexistence of solutions we also obtain results of a quantitative nature, as in the determination of the number of representations of an integer as the sum of four squares. All of the equations considered in this chapter are classical, each playing an important role in the historical development of the subject.


Rational Point Nontrivial Solution Rational Solution Integral Solution Diophantine Equation 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Kenneth Ireland
  • Michael Rosen
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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