Hi, I was wondering if anyone could recommend a good book on number theory that goes into a decent amount of depth? Preferably aimed at people with A-level maths plus a bit of undergraduate discrete maths or something like that. I would prefer that the book covers as many big areas as possible, though I don't want a book that tells you about something interesting, then doesn't proceed to explain it. I thought it might be worth asking PE people since many of you have probably read a few and can recommend some good ones.

Many thanks.

## A good number theory book?

### Re: A good number theory book?

I only have two books on the subject. It's been ages since I read them, so my description is mostly from memory:

The classic book is "An introduction to the Theory of Numbers" by Hardy and Wright (Oxford University Press). (link)

It is dense and old fashioned, but contains a very large amount of material and proves everything it states. This is the granddaddy of all Number Theory books, and it has been continuously in print for nearly 75 years, now in its 6th edition.

More fun to dip into for a beginner is the other book I have - "Recreations in the Theory of Numbers", by Albert Beiler (Dover). (link)

Less formal than the other (but still old fashioned as it is also quite an old book), and less in depth, but very interesting, varied, and well written. It is just the kind of stuff that helps you with the Project Euler problems . It does not always rigorously prove everything it states, but usually contains enough explanation to show its truthfulness so that you could write down a formal proof if you wanted to. It's quite cheap too as it is printed by Dover publications.

The classic book is "An introduction to the Theory of Numbers" by Hardy and Wright (Oxford University Press). (link)

It is dense and old fashioned, but contains a very large amount of material and proves everything it states. This is the granddaddy of all Number Theory books, and it has been continuously in print for nearly 75 years, now in its 6th edition.

More fun to dip into for a beginner is the other book I have - "Recreations in the Theory of Numbers", by Albert Beiler (Dover). (link)

Less formal than the other (but still old fashioned as it is also quite an old book), and less in depth, but very interesting, varied, and well written. It is just the kind of stuff that helps you with the Project Euler problems . It does not always rigorously prove everything it states, but usually contains enough explanation to show its truthfulness so that you could write down a formal proof if you wanted to. It's quite cheap too as it is printed by Dover publications.

_{Jaap's Puzzle Page}

- euler
- Administrator
**Posts:**3478**Joined:**Sun Mar 05, 2006 4:49 pm**Location:**Cheshire, England-
**Contact:**

### Re: A good number theory book?

I have quite a few, but I think that "Number Theory" by George E. Andrews is an excellent choice. It only has about 250 pages, but it is deceptively in-depth and covers a wide variety of elementary concepts rigorously. It also includes useful exercises (there are hints and answers for selected exercises). There aren't any reviews on amazon.co.uk, but the site now import reviews from amazon.com which should give you useful thoughts from other readers.

http://www.amazon.co.uk/Number-Theory-D ... 486682528/

http://www.amazon.co.uk/Number-Theory-D ... 486682528/

*impudens simia et macrologus profundus fabulae*

- PurpleBlu3s
**Posts:**75**Joined:**Mon Sep 19, 2011 6:49 pm

### Re: A good number theory book?

Thanks for your posts. I've decided to get Hardy and Wright's book for now.

### Re: A good number theory book?

I know you must have learnt everything by now on number theory but I still would recommend you this "elementary number theory" a tata McGraw hill book