Number theory book recommendation.
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?
Solution 1:
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.
Solution 2:
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.
Solution 3:
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.
Solution 4:
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.