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More About This Textbook
Overview
Number theory is concerned with the properties of the natural numbers: 1,2,3,.... During the seventeenth and eighteenth centuries, number theory became established through the work of Fermat, Euler and Gauss. With the hand calculators and computers of today, the results of extensive numerical work are instantly available and mathematicians may traverse the road leading to their discoveries with comparative ease. Now in its second edition, this book consists of a sequence of exercises that will lead readers from quite simple number work to the point where they can prove algebraically the classical results of elementary number theory for themselves. A modern high school course in mathematics is sufficient background for the whole book which, as a whole, is designed to be used as an undergraduate course in number theory to be pursued by independent study without supporting lectures.
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Table of Contents
Preface to the second edition; Introduction; 1. The fundamental theorem of arithmetic; 2. Modular addition and Euler's Phi function; 3. Modular multiplication; 4. Quadratic residues; 5. The equation xn+yn=zn, for n=2, 3, 4; 6. Sums of squares; 7. Partitions; 8. Quadratic forms; 9. Geometry of numbers; 10. Continued fractions; 11. Approximation of irrationals by rationals; bibliography; Index.