This text begins with a discussion of general lemmas and advances to an investigation of Waring's problem, including explorations of singular series, the contribution of the basic intervals, and an estimate for G(n). Further topics include approximation by the fractional parts of the values of a polynomial, estimates for Weyl sums, much more. 1954 edition. Unabridged republication of the edition published by Interscience, New York, 1954.
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
Essays on the Theory of Numbers by Richard Dedekind Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.
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.
