Fermat's and Euler's theorems, what class of math do they fall into?

Question

I am getting quick and dirty lessons on mathematics involving operation based on Fermat and Euler's Theorems, along with Chinese Remainder Theorems, with their usage in modern cryptography. My comprehension would be better if I could school myself in the basics leading up to these. What type of mathematics categories would these theorems be classified into, and does anyone recommend any texts?

I am referring to the theorems regarding the use of modulus, primitive roots, exponentiation and Discrete Log Problems.

Answer 1

There are at least 3 different Fermat theorems that I can think of. One is in calculus. Another known as Fermat's little theorem is in Number theory and abstract algebra. The most famous one Fermat's last theorem is in number theory. There are Euler's theorms in number theory and abstract algebra. The Chinese Remainder theorem is in Abstract algebra and number theory.

I own a number theory book by Andrews, it is a dover book (so it is cheap) and it is good.

As for abstract algebra, I like Dummit and Foote. It is a graduate level book. For undergrad, Gallian's Contemporary Abstract Alg is good.

Hope this helps.

Answer 2

Euclidean Geometry

Answer 3

I'm not familiar with them but it sounds like number theory to me.