Number theory book recommendation.

Question

I'm currently trained in Algebra, Calculus and Statistics in high school level. Basically, I've no knowledge at all in number theory as this subject is not taken seriously in my country.

I was thinking to self-learning number theory by books. But the books I found in the internet are really hard and complicated for me as I've no number theory background at all.

Recently, I was asked by a 10 years old kid for a question which is related to number theory. I've no idea at all how to solve that, it was really embarrassed.

So can anyone recommend me some books for number theory which are suitable for me?

A short, easy book on number theory at the high school level is Invitation to Number Theory by Oystein Ore. — user49640, Jun 07 '17 at 08:51
Does this answer your question? Good Number Theory books to start with? — , Feb 01 '21 at 19:15
Does this answer your question? Books on Number Theory for Layman — user1147844, Jun 06 '23 at 07:28

score 10 · Accepted Answer · answered Jun 07 '17 at 07:41

10

The greatest of all classical books on this subject is An Introduction to the Theory of Numbers, by G. H. Hardy and Edward M. Wright.

answered Jun 07 '17 at 07:41

José Carlos Santos

427,504

score 7 · Answer 2 · answered Mar 01 '20 at 18:55

I am writing the books in their increasing order of difficulty (my personal experience) for a beginner in number theory.

Level A:

A Friendly Introduction to Number Theory by Joseph H. Silverman. (This is the easiest book to start learning number theory.)

Level B:

Elementary Number Theory by David M Burton.

The Higher Arithmetic by H. Davenport

Elementary Number Theory by Gareth A. Jones

Level C:

An introduction to the theory of numbers by Niven, Zuckerman, Montgomery.

An Introduction to the Theory of Numbers by G. H. Hardy and Edward M. Wright.

Level D:

A Classical Introduction to Modern Number Theory by Ireland and Rosen.

+1 for nice arrangements of books as per difficulty...., As a beginner when I start the *An Introduction to the Theory of Numbers by G. H. Hardy and Edward M. Wright* then some notation of that books were little bit challenging for me to understand — , Jul 10 '22 at 17:50

D_S · Answer 3 · 2017-06-08T13:32:32.990

3

A Classical Introduction to Modern Number Theory by Ireland and Rosen.

Fantastic undergraduate book that covers a lot of ground. While it doesn't require much background, many of the proofs are terse and the authors expect a lot out of you. But it's a very rewarding read and in addition to the number theory you will learn, this book will greatly improve your ability to read mathematics.

edited Jun 08 '17 at 13:32

answered Jun 08 '17 at 12:57

D_S

33,891

Américo Tavares · Answer 4 · 2017-06-08T12:55:20.137

2

The Higher Arithmetic: An Introduction to the Theory of Numbers by Harold Davenport

Introduces the classic concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers

and Elementary Number Theory by Sierpinski

The variety of topics covered (...) includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian integers.

edited Jun 08 '17 at 12:55

answered Jun 07 '17 at 18:58

Américo Tavares

38,602

1

I think Davenport's book covers great introductory topics and contains many gems, but the style of the book is not well suited to a first-time student (surprising, given the title and aim). In some proofs the choice of which steps are detailed and which are omitted leads to more obfuscation than clarity for a first-time student (see the proof of quadratic reciprocity). The new student hopes to gain a better "feel" for the subject with such a conversational style, but I think that for every point where this succeeds, it causes enough trouble in other places that ultimately it is not worth it. – Jonathan Rayner Jul 08 '19 at 14:46
1

To provide a counterpoint to my own comment: Davenport is incredible for an early student to learn "about" Number Theory as a field - it does an excellent job of mentioning "big" open problems that have simple formulations, the history and motivating questions that lead to be more abstract modern formulations, and so on. These are the types are things that are exciting for first-time students and that is a good strength. – Jonathan Rayner Jul 08 '19 at 14:51

score 1 · Answer 5 · edited Aug 27 '23 at 15:36

1

In my opinion the best way to start learning this subject would be "Elementary Number Theory" by Jones & Jones

As far as I can remember this has prequisites really.

edited Aug 27 '23 at 15:36

J. W. Tanner

60,406

answered Oct 28 '18 at 12:13

Trajan

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score 0 · Answer 6 · answered Jun 07 '17 at 07:51

0

For Elementary number theory, I would recommend David M. Burton's Elementary number theory and for a bit higher studies my choice is An introduction to theory of numbers by Niven, Zuckerman, Montgomery

answered Jun 07 '17 at 07:51

Vidyanshu Mishra

10,143

score 0 · Answer 7 · answered Jun 07 '17 at 09:05

0

I would recommend David my Burton elementary number theory. Most mathematicians prefer it for starting.A very concise and at the same time complete book

answered Jun 07 '17 at 09:05

vutsuak

9

1

Simon Plouffe is a very prominent mathematician (of 'Borwein Bailey Plouffe' fame, if that rings any bells) and it seems highly unlikely (though admittedly not impossible) that he'd be hosting an illegal copy. – Steven Stadnicki Jun 07 '17 at 19:02

score 0 · Answer 8 · answered Jun 08 '17 at 13:00

Another good option is:

B. Fine and G. Rosenberger, Number Theory: An Introduction via the Density of Primes

From Amazon review: "All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes."

score 0 · Answer 9 · answered Dec 30 '21 at 13:25

0

You may take a look at the Number Theory section of MAA Reviews:

https://www.maa.org/press/maa-reviews/browse?field_tags_tid=37227

answered Dec 30 '21 at 13:25

duje

433

score -1 · Answer 10 · answered Jun 07 '17 at 11:48

-1

I had good experience with the Number theory book by Borevich and Shafarevich.

answered Jun 07 '17 at 11:48

Mikhail Katz

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Number theory book recommendation.

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