Solving the Pell Equation

• Κύριοι συγγραφείς: Jacobson, Michael J. (Συγγραφέας), Williams, Hugh C. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2009.
• Σειρά: CMS Books in Mathematics,
• Θέματα: Mathematics.; Number theory.; Ecotoxicology.; Number Theory.

Pell's equation is a very simple, yet fundamental Diophantine equation which is believed to have been known to mathematicians for over 2000 years. Because of its popularity, the Pell equation is often discussed in textbooks and recreational books concerning elementary number theory, but usually...

Πίνακας περιεχομένων:

• Early History of the Pell Equation
• Continued Fractions
• Quadratic Number Fields
• Ideals and Continued Fractions
• Some Special Pell Equations
• The Ideal Class Group
• The Analytic Class Number Formula
• Some Additional Analytic Results
• Some Computational Techniques
• (f, p) Representations of -ideals
• Compact Representations
• The Subexponential Method
• Applications to Cryptography
• Unconditional Verification of the Regulator and the Class Number
• Principal Ideal Testing in
• Conclusion.