Good self-teaching book for elementary and advanced number theory?

[RossH]

Hello. I am looking for learning materials for the field of number theory. I took a class this semester in number theory and the topic fascinated me, but I don't feel like I learned that much. I am a mathematics minor so I have a very strong background in basic math, abstract/linear algebra, and calculus, but in number theory I don't get much beyond Diophantine equations. So, do you have any book recommendations? My only requirements are that the books are inexpensive (so no current textbooks) and that the answers to at least some of the questions are in the book. I don't want to have to Google for answers to every question in any chapter. Thanks for the help!

 

[Gib Z]

Try to find "Introduction to the theory of Numbers" by Hardy and Wright in a university library. It's not cheap but it is the classic in the field and most universities have at least one, if not several, copies of that on shelf.

 

[Petek]

Hardy and Wright is a classic and would be a good choice as a second text in number theory. The most recent edition (sixth) is available on https://www.amazon.com/dp/0199219869/?tag=pfamazon01-20. You could download one or more of these to get exercises. I don't know right offhand whether any of these books have solutions, though. You could post your solutions on this forum to see if they are correct.

If you buy Hardy and Wright, you may wish to look at http://www.maths.ox.ac.uk/groups/number-theory/errata-hardy-and-wright, which has a list of misprints with corrections.

 

[lapin]

Send me your email and I will send you my book for free!

 

[rezeew]

Hi there,

I can definitely recommend a few books for you to explore in the field of number theory. For elementary level, I would suggest "Number Theory: A Lively Introduction with Proofs, Applications, and Stories" by James Pommersheim, Tim Marks, and Erica Flapan. This book is written in an engaging and accessible style, making it a great self-teaching resource for beginners. It covers a wide range of topics including prime numbers, congruences, and Diophantine equations.

For more advanced level, I would recommend "An Introduction to the Theory of Numbers" by G.H. Hardy and E.M. Wright. This classic book is a comprehensive and rigorous introduction to number theory, covering topics such as prime number theorem, quadratic forms, and continued fractions. It is a bit more challenging, but it is a great resource for those looking to deepen their understanding of the subject.

Both of these books are reasonably priced and have answers to some of the questions in the book, so you won't have to rely on external sources for every question. I hope you find these recommendations helpful in your self-teaching journey in number theory. Happy learning!