Elementary Number Theory

Got the book for free in electronic format. The prices for these books are criminal. Intellectual property is the fraud of frauds. The book itself is excellent. I had not had any formal study of proofs when I started reading, but this book guides you very gently and clearly through the process. Number theory is NOT boring, and going through this book will make you feel enlightened. It's not easy, but very doable for anyone of average intelligence.

This is a textbook about Elementary Number Theory, where "elementary" does not mean "simple" or "beginning", but rather those portions of the mathematics of integers that do not rely on analysis (infinitesmal calculus). Number theory allows many different orderings of topics, without omitting proofs. I found Burton's order to be easy to follow. Many results in number theory follow easily from results in abstract algebra or linear algebra. The author does not depend on results beyond elementary algebra, but some degree of mathematical maturity is required. Readers with a math degree will still have to work to absorb the material. There are many problems. Those with numerical answers are answered in the back of the book. About half of the others are answered in an answer guide, available separately. Almost everything is proved. I only recall two cases of "left to the reader" except for the problems, of course. None of the problems are used for future developments in the main text. The author has a separate text about the history of mathematics. Most of the chapters in this book start with a section about the history of the material in the chapter and about the people that developed it. This is interesting extra material, or padding that makes the book even more expensive than it should be, depending on you. This is the 6th edition. The only error I encountered was a consistent misspelling of one name in chapter 10. I could not find any reported errors on the WWW. I've used several other number theory books over the years. This one seems the best for me. Perhaps that is due to Burton's skill, or perhaps it is because I finally worked through one from front to back, instead of searching for the information I needed just then.

I'm a first-year Ph.D. student, taking a graduate-level number theory course, and I still use this book from my undergrad years as a reference. Just about any basic number theory topic you're looking for is in here. I can't recommend it highly enough!

This book is the best introduction to number theory that I have found. I only have single maths A Level, but found this book extremely easy to get into. It starts out with gcd lcm stuff, then introduces modular arithmetic and chinese remainder theorem; it does some other things as well (I forget), and then goes on to fermat's little theorem and wilson's theorem...then does lots of other things like 'arithmetic functions' and continued fractions, quadratic residues...which I haven't got to yet. Certainly, it doesn't look as though it's going t get any more difficult in this book, and the excersises are realistic (if a little too simple)Anyone who cannot work through this book should not be studying maths. The book surely covers most first year degree courses.I should also say that there are about 14 chpters in the book, even though I have only described the first 7 or so; the book also gives a history of maths, with short passages about famous mathmos like Gauss, Euclid, diaphantus. About 300 pages in total, loads of examples, plenty of spaces for rough working (big margins). What more can I say? Buy it.

This is an excellent textbook for an introductory course in Number Theory. I have used it a number of times for my own courses and I believe it is the most popular book for elementary Number theory courses in the United States. It covers all the standard topics in Number Theory including congruences, properties of prime numbers and their distribution, the theorems of Fermat and Wilson, quadratic residues, quadratic reciprocity, perfect numbers, pythagorian triples, representation of integers as sums of squares and a chapter on continued fractions and Pell's equation. The book includes historical notes, useful tables and a great number of interesting exercises. I recommend this book for begginers in Number Theory but I believe that even the advanced reader may find something interesting.