Jacobson M.J., Williams H.C. Solving the Pell Equation

Springer, 2009. — 520 p. — ISBN: 038784922XPell's Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell's Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation.
The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell's Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.Книга "Solving the Pell Equation" подробно раскрывает теорию квадратичных полей, теорию идеалов, а также её приложение к задаче поиска рационального решения уравнения Пелля при различных значениях параметра D:
x^2-D*y^2=+1 (или -1).
Особое внимание уделяется решению уравнения при больших значениях D, а также прикладных аспектах решения уравнения в криптографии. Присутствует множество описаний алгоритмов.