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The Pell Equation, written by Edward Everett Whitford and originally published in 1912, is a mathematical treatise that focuses on the Pell equation, a type of Diophantine equation named after the English mathematician John Pell. The book provides a comprehensive overview of the history, theory, and applications of the Pell equation, which takes the form of x^2 - dy^2 = 1, where d is a positive integer that is not a perfect square. Whitford begins by discussing the origins of the Pell equation and its relationship to other Diophantine equations, such as the quadratic equation. He then delves into the mathematical properties of the Pell equation, including its solutions, fundamental solutions, and continued fractions. The book also covers the use of the Pell equation in number theory, geometry, and cryptography, as well as its connections to other areas of mathematics, such as algebraic number theory and elliptic curves.Throughout the book, Whitford provides numerous examples and exercises to help readers understand and apply the concepts presented. He also includes historical notes and biographical sketches of prominent mathematicians who contributed to the development of the Pell equation. Overall, The Pell Equation is a valuable resource for mathematicians, students, and anyone interested in the history and theory of Diophantine equations.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world’s literature in affordable, high quality, modern editions, that are true to their original work.
