# Foundations of number theory

Differently from the other paths, each of which has the goal of proving one specific theorem, the goal of this path is simply to convey a general knowledge of number theory, limited to the aspects which are mostly connected with prime numbers. We’ll treat the following main subjects:

• Definition of prime number
• Study of binomial coefficients
• Statement and proof of the Bertrand’s Postulate
• Study of the functions $\theta(x)$, $\psi(x)$ and $\pi(x)$
• Statement and proof of Chebyshev’s Theorem, both tha weak version and the strong version
• Study of the harmonic series
• Study of the factorial
• Statement of the Prime Number Theorem

## The path

In order to create this path, we selected from the other paths the posts which we regard as important for a general study of number theory. So, every post listed below belongs to at least one of the other paths.