Book Suggestions - Primes, number theory, modular arithmetic

Question

I am looking for introductory level books.

For example, something that could prepare me for diving into modular arithmetic. I am learning a bit on my own, but I definitely am lacking in background information about primes, their relationship to each other, etc.

More specifically, something that provides enough information for me to prove common problems such as...

If a and b are relatively prime...

There are always integers s and t such that...

sa + tb = 1

Thanks in advance...

Answer 1

I would suggest you pick a copy of Hardy's Introduction to the theory of numbers. I think he recalls most arithmetic basics (like the fundamental arithmetic theorem etc) in the beginning of the book.

Answer 2

You may want to have a look at “What is Mathematics? An Elementary Approach to Ideas and Methods” by Richard Courant and Herbert Robbins.

It’s very well written though it only has an introductory coverage of number theory. Nonetheless, it’s a good place that start.

A classical introduction to number theory by Rosen is a much more thorough book though not beginner friendly.