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.