Irreducible Polynomials in Ζ[x]

Abstract

If we express a prime in base b≥2 as, p = a_nb^n + a_(n−1)b^(n−1) + · · · + a_1b + a_0, then the polynomial f(x) = a_nx^n + a_(n−1)x^(n−1) + · · · + a_1x + a_0 is necessarily irreducible in Ζ[x].

In this thesis, we reprove adding precise details about this theorem and using this result, we make an example for a prime number p in base b=2 and b＞2.