Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, ... and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and much else besides. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat’s last theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises. John J. Watkins is Professor Emeritus of Mathematics at Colorado College. His books include Number Theory: A Historical Approach, Across the Board: The Mathematics of Chessboard Problems, and Topics in Commutative Ring Theory. Robin Wilson is Emeritus Professor of Pure Mathematics at the Open University, UK. He has written and edited over 40 books on a range of mathematical topics. He has been awarded two prizes by the MAA for his ’outstanding expository writing.’ Together they have written Graphs: An Introductory Approach and edited Combinatorics: Ancient & Modern. OYSTEIN ORE was born in Oslo, Norway, in 1899. After graduating from the University of Oslo, he continued his mathematical studies at the University of Gottingen in Germany and at the Mittag-Leffler Institute in Sweden and received his Ph.D. degree in Oslo in 1942. His career in the United States began in 1927 at Yale University where he became professor of mathematics and where, from 1931, he was Sterling Professor. He was Chair of the mathematics department from 1939 to 1942. In addition to over 100 mathematical research papers, he wrote several books, including Number Theory and its History; Cardano, the Gambling Scholar; Niels Henrik Abel, Mathematician Extraordinary; Theory of Graphs; and (for the MAA) Graphs and their Uses. He died in Oslo in 1968.

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