Identifiant pérenne de la notice : 206749430
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Note publique d'information : 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 not in much depth. This book provides a modern
and deeper approach to the problem of solving the Pell equation. The main component
of this will be computational techniques, but in the process of deriving these it
will be necessary to develop the corresponding theory. One objective of this book
is to provide a less intimidating introduction for senior undergraduates and others
with the same level of preparedness to the delights of algebraic number theory through
the medium of a mathematical object that has fascinated people since the time of Archimedes.
To achieve this, this work is made accessible to anyone with some knowledge of elementary
number theory and abstract algebra. Many references and notes are provided for those
who wish to follow up on various topics, and the authors also describe some rather
surprising applications to cryptography. The intended audience is number theorists,
both professional and amateur, and students, but we wish to emphasize that this is
not intended to be a textbook; its focus is much too narrow for that. It could, however
be used as supplementary reading for students enrolled in a second course in number
theory
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