Superb introduction for readers with limited formal mathematical training. Topics include Euclidean algorithm and its consequences, congruences, powers of an integer modulo m, continued fractions, Gaussian integers, Diophantine equations, more. Carefully selected problems included throughout, with answers. Only high school math needed. Bibliography.
Here's a sample of other books in this Dover category
Recreations in the Theory of Numbers by Albert H. Beiler Number theory proves to be a virtually inexhaustible source of intriguing puzzle problems. Includes divisors, perfect numbers, the congruences of Gauss, scales of notation, the Pell equation, more. Solutions to all problems.
Excursions in Number Theory by C. Stanley Ogilvy, John T. Anderson Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. ". . . splendidly written, well selected and presented collection . . ." — Martin Gardner.
An Adventurer’s Guide to Number Theory by Richard Friedberg This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.
Number Theory and Its History by Oystein Ore Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
Number Theory by George E. Andrews Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more
Fundamentals of Number Theory by William J. LeVeque Basic treatment, incorporating language of abstract algebra and a history of the discipline. Unique factorization and the GCD, quadratic residues, sums of squares, much more. Numerous problems. Bibliography. 1977 edition.
Continued Fractions by A. Ya. Khinchin Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Properties of the apparatus, representation of numbers by continued fractions, more. 1964 edition.
