This second volume is a comprehensive treatment of Diophantine analysis. Besides the familiar cases of Diophantine equations, this rubric also covers partitions, representations as a sum of two, three, four or $n$ squares, Waring's problem in general and Hilbert's solution of it, and perfect squares in artihmetical and geometrical progressions. Many important Diophantine equations, such as Pell's equation, and classes of equations, such as quadratic, cubic and quartic equations, are treated in detail.

Covers the related topics of divisibility and primality. This book describes the development of our understanding of perfect numbers. It also covers standard topics, such as Fermat's theorems, primitive roots, counting divisors, the Mobius function, and prime numbers themselves.