Algorithmic Number Theory: Efficient Algorithms v. 1

Algorithmic Number Theory provides a thorough introduction to the design and analysis
of algorithms for problems from the theory of numbers. Although not an elementary textbook, it
includes over 300 exercises with suggested solutions. Every theorem not proved in the text or left
as an exercise has a reference in the notes section that appears at the end of each chapter. The
bibliography contains over 1,750 citations to the literature. Finally, it successfully blends
computational theory with practice by covering some of the practical aspects of algorithm
implementations.The subject of algorithmic number theory represents the marriage of number theory
with the theory of computational complexity. It may be briefly defined as finding integer solutions
to equations, or proving their non-existence, making efficient use of resources such as time and
space. Implicit in this definition is the question of how to efficiently represent the objects in
question on a computer. The problems of algorithmic number theory are important both for their
intrinsic mathematical interest and their application to random number generation, codes for
reliable and secure information transmission, computer algebra, and other areas.Publisher's Note:

Volume 2 was not written. Volume 1 is, therefore, a stand-alone publication.