An Introduction to the Theory of Numbers

An Introduction to the Theory of Numbers - The Trillia...

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The Trillia Lectures on Mathematics An Introduction to the Theory of Numbers 9 781931 705011
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The Trillia Lectures on Mathematics An Introduction to the Theory of Numbers Leo Moser The Trillia Group West Lafayette, IN
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Terms and Conditions You may download, print, transfer, or copy this work, either electronically or mechanically, only under the following conditions. If you are a student using this work for self-study, no payment is required. If you are a teacher evaluating this work for use as a required or recommended text in a course, no payment is required. Payment is required for any and all other uses of this work . In particular, but not exclusively, payment is required if (1) you are a student and this is a required or recommended text for a course; (2) you are a teacher and you are using this book as a reference, or as a required or recommended text, for a course. Payment is made through the website http://www.trillia.com . For each individual using this book, payment of US$10 is required. A sitewide payment of US$300 allows the use of this book in perpetuity by all teachers, students, or employees of a single school or company at all sites that can be contained in a circle centered at the location of payment with a radius of 25 miles (40 kilometers). You may post this work to your own website or other server (FTP, etc.) only if a sitewide payment has been made and it is noted on your website (or other server) precisely which people have the right to download this work according to these terms and conditions. Any copy you make of this work, by any means, in whole or in part, must contain this page, verbatim and in its entirety. An Introduction to the Theory of Numbers c circlecopyrt 1957 Leo Moser ISBN 1-931705-01-1 Published by The Trillia Group, West Lafayette, Indiana, USA First published: March 1, 2004. This version released: March 31, 2009. The phrase “The Trillia Group” and The Trillia Group logo are trademarks of The Trillia Group. This book was prepared by William Moser from a manuscript by Leo Moser. We thank Sinan Gunturk, Joseph Lipman, and Mark Hudson for proofreading parts of the manuscript. We intend to correct and update this work as needed. If you notice any mistakes in this work, please send e-mail to [email protected] and they will be corrected in a later version.
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Contents Preface ................................................................... v Chapter 1. Compositions and Partitions .............................. 1 Chapter 2. Arithmetic Functions ...................................... 7 Chapter 3. Distribution of Primes ................................... 17 Chapter 4. Irrational Numbers ....................................... 37 Chapter 5. Congruences .............................................. 43 Chapter 6. Diophantine Equations ................................... 53 Chapter 7. Combinatorial Number Theory .......................... 59 Chapter 8. Geometry of Numbers ................................... 69 Classical Unsolved Problems ........................................... 73 Miscellaneous Problems ................................................ 75 Unsolved Problems and Conjectures .................................. 83
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Preface These lectures are intended as an introduction to the elementary theory of numbers. I use the word “elementary” both in the technical sense—complex variable theory is to be avoided—and in the usual sense—that of being easy to understand, I hope.
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