Number theory, the Queen of Mathematics, is an almost purely theoretical
science. Yet it can be the source of endlessly intriguing puzzle
problems, as this remarkable book demonstrates. This is the first book
to deal exclusively with the recreational aspects of the subject and it
is certain to be a delightful surprise to all devotees of the
mathematical puzzle, from the rawest beginner to the most practiced
expert. Almost every aspect of the theory of numbers that could
conceivably be of interest to the layman is dealt with, all from the
recreational point of view. Readers will become acquainted with
divisors, perfect numbers, the ingenious invention of congruences by
Gauss, scales of notation, endless decimals, Pythagorean triangles
(there is a list of the first 100 with consecutive legs; the 100th has a
leg of 77 digits), oddities about squares, methods of factoring,
mysteries of prime numbers, Gauss's Golden Theorem, polygonal and
pyramidal numbers, the Pell Equation, the unsolved Last Theorem of
Fermat, and many other aspects of number theory, simply by learning how
to work with them in solving hundreds of mathematical puzzle problems.
The text is extremely clear and easy to follow, and it bears convincing
evidence of the author's deep sense of humor and his outstanding ability
to lure the reader through even the most difficult trails by skillfully
revealing their fascination. The problems distributed throughout the
book are explained in the final chapter and there is also a
supplementary chapter containing 100 problems and their solutions, many
original. There are over 100 tables.
The appeal of these stimulating puzzles lies in their ready
comprehensibility and the fact that only high school math is needed to
master the fundamental theory presented by the author. This theory is
itself interesting and of use to the more serious math student, but it
may be omitted by lay readers without diminishing the book's challenge
or detracting from the pleasure-giving nuggets it contains.
