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

Map of paths for number theory
General introduction to paths

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 other path.