Elementary number theory - prerequisites

Solution 1:

I will do exactly the same thing. I just finished my degree in mathematics but in our department there is not a single course of Number Theory, and since I will start my graduate courses in October I thought it will be a great idea to study Number Theory on my own. So, I asked one of my professors, who is interested in Algebraic Geometry and Number Theory, what would be a textbook that has everything an undergraduate should know about Number Theory before moving on. He told me that A Classical Introduction to Modern Number Theory by Kenneth F. Ireland and Michael Rosen is the perfect choice. He also mentioned that I should definitely study chapters 1-8,10-13 and 17. Another book that he mentioned was A Friendly Introduction to Number Theory by Joseph H. Silverman. He emphasized though that this book is clearly an introduction whereas the previous one gives you all the tools you need in order to study many things that are connected to Number Theory. I hope that this helped you!

Solution 2:

In my opinion Hardy &Wright's book on Number Theory is not the best possible book for someone "who has no prior training in Number Theory", I would suggest the following books.

• Elementary Number theory by David M. Burton.

• Number Theory A Historical Approach by John H. Watkins

• Higher Arithmetic by H. Davenport

All the books are well-written. I think that if you are a beginner, and if you are interested in the historical aspects of Number Theory as well, you may first look at the second book. Although Burton's books also have some historical background in each chapter. I would suggest reading Davenport's books a bit later when you have a fair grasp of the subject.

Also I suggest you to look at the suggestions given at this post.

Solution 3:

One of the best is An Introduction to the Theory of Numbers by Niven, Zuckerman, and Montgomery.