An Introduction to Number Theory

In general, this book gives a comprehensive account on elementary number theory. The first few chapters include some fundamental concepts like divisibility and congruences (i.e. a simple kind of modular arithmetic), as well as famous yet basic theorems like the fundamental theorem of arithmetic. Important topics in number theory such as Diophantine equations, fractional approximations for irrational numbers and Quadratic fields are there, and if you're interested in magic squares, I'd like to say that a whole chapter is devoted to it. There're some good points featuring this book. It assumes no prerequisite in number theory. Just a bit knowledge about numbers and operations on them are needed. Results and theorems are closely related, allowing you to observe how things are connected. Although not many examples are available, some are really instructive and helpful enough to avoid misconceptions. However, it's a pity to say that the materials contained are not really well-organized, especially those in Chapter 7: the geometric arguments used in the development of the continued fraction algorithm lack concision, and a few proofs are quite annoying because the author failed to justify some claims that shuold not be treated as something "obvious". It can be motivating just to provide readers guidelines about how to work out those minor stuff, but such things shouldn't have been misleadingly called "proofs". Another problem is that the illustratons presented are occasionally insufficient, and this is particularly the case in the chapter about Diophantine equations. Novices in the subject can hardly rely on the text to solve harder exercises contained without tracing out more technique which is not emphasized. Overall, the book deserves to be a fine reading for the interested ones new to number theory. But if you're serious about the topic, find an even better book instead.