In this book, we cover the basics of elementary number theory. Topics begin with natural numbers, divisibility in the integers, and unique prime factorization. After that, we cover linear, quadratic, and polynomial congruence equations. While studying these topics we'll also learn how to use python. In the second part, we introduce automating proofs in elementary number theory using python. We'll do this by first studying Grobner Bases in polynomial rings and then making a connection between these rings and theorems involving integer divisibility.