Solving the Pell Equation

Authors:

ISBN: 978-0-387-84922-5 (Print) 978-0-387-84923-2 (Online)

Table of contents (17 chapters)

  1. Front Matter

    Pages i-xx

  2. No Access

    Chapter

    Pages 1-17

    Introduction

  3. No Access

    Chapter

    Pages 19-41

    Early History of the Pell Equation

  4. No Access

    Chapter

    Pages 43-73

    Continued Fractions

  5. No Access

    Chapter

    Pages 75-96

    Quadratic Number Fields

  6. No Access

    Chapter

    Pages 97-124

    Ideals and Continued Fractions

  7. No Access

    Chapter

    Pages 125-152

    Some Special Pell Equations

  8. No Access

    Chapter

    Pages 153-184

    The Ideal Class Group

  9. No Access

    Chapter

    Pages 185-207

    The Analytic Class Number Formula

  10. No Access

    Chapter

    Pages 209-235

    Some Additional Analytic Results

  11. No Access

    Chapter

    Pages 237-264

    Some Computational Techniques

  12. No Access

    Chapter

    Pages 265-283

    (f, p) Representations of \(\mathcal{O}\) -ideals

  13. No Access

    Chapter

    Pages 285-305

    Compact Representations

  14. No Access

    Chapter

    Pages 307-352

    The Subexponential Method

  15. No Access

    Chapter

    Pages 353-386

    Applications to Cryptography

  16. No Access

    Chapter

    Pages 387-404

    Unconditional Verification of the Regulator and the Class Number

  17. No Access

    Chapter

    Pages 405-421

    Principal Ideal Testing in \(\mathcal{O}\)

  18. No Access

    Chapter

    Pages 423-437

    Conclusion

  19. Back Matter

    Pages 439-495