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The Theory of Numbers by Robert D. Carmichael
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The Theory of Numbers written by
The purpose of this little book is to give the reader a convenient introduction to the theory of numbers, one of the most extensive and most elegant disciplines in the whole body of mathematics. The arrangement of the material is as follows:
The first five chapters are devoted to the development of those elements which are essential to any study of the subject. The sixth and last chapter is intended to give the reader some indication of the direction of further study with a brief account of the nature of the material in each of the topics suggested. The treatment throughout is made as brief as is possible consistent with clearness and is confined entirely to fundamental matters. This is done because it is believed that in this way the book may best be made to serve its purpose as an introduction to the theory of numbers.
Numerous problems are supplied throughout the text. These have been selected with great care so as to serve as excellent exercises for the student’s introductory training in the methods of number theory and to afford at the same time a further collection of useful results. The exercises marked with a star are more difficult than the others; they will doubtless appeal to the best students.
(Robert D. Carmichael)
Book Detail :-
Title: The Theory of Numbers
Author(s): Robert Daniel Carmichael
Publisher: John Wiley and Sons
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About Author :-
Author Robert Daniel Carmichael (1848-1928), Associate Professor of Mathematics in Indiana University, NEW YORK.
He earned his bachelor's degree in 1898, while he was studying towards his Ph.D. degree at Princeton University. Carmichael completed the requirements for his Ph.D. in mathematics in 1911. Carmichael's Ph.D. research in mathematics was done under the guidance of the noted American mathematician G. David Birkhoff, and it is considered to be the first significant American contribution to the knowledge of differential equations in mathematics.
Carmichael is known for his research in what are now called the Carmichael numbers (a subset of Fermat pseudoprimes, numbers satisfying properties of primes described by Fermat's Little Theorem although they are not primes), Carmichael's totient function conjecture, Carmichael's theorem, and the Carmichael function, all significant in number theory and in the study of the prime numbers.
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Book Contents :-
The Theory of Numbers written by
cover the following topics.
1. ELEMENTARY PROPERTIES OF INTEGERS
2 ON THE INDICATOR OF AN INTEGER
3 ELEMENTARY PROPERTIES OF CONGRUENCES
4 THE THEOREMS OF FERMAT AND WILSON
5 PRIMITIVE ROOTS MODULO m.
6 OTHER TOPICS
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