Solving the Pell Equation

• 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.

From the reviews: "'Solving the Pell Equation' is a ... monograph that offers encyclopedic in-depth coverage of its topic. ... The book is very well-written and filled with many interesting asides. ... As one of the book's stated goals is to provide 'a relatively gentle introduction for senior undergraduates,' a much larger set of examples ... increase the number of students at every level who could profitably read this text. ... I highly recommend the book to anyone with an interest in Pell's equation and its modern study." (Thomas Hagedorn, The Mathematical Association of America, July, 2009) "This new book on the Pell equation, eagerly anticipated by the mathematical community and written by two active contributers to the field of computational number theory in general and to Pell's equation in particular, exposes the ongoing interaction between modern computational number theory and practice in a way that is pleasant to read and to study, and that is readily accessible to conscientious undergraduate students. ... this book is highly recommended." (Robert Juricevic, Mathematical Reviews, Issue 2009 i) "Pell's equation is best known for the misattribution by Euler of a method of solution to John Pell. ... This work will be valuable for a comprehensive mathematics library to give strong mathematics students a motivated, deep introduction to advanced number theory. Summing Up: Recommended. Lower- and upper-division undergraduates." (J. McCleary, Choice, Vol. 47 (5), January, 2010)