The Baker Theorem

Abstract

A complex number $\alpha$ is called algebraic number  if there exists a non-zero polynomial $f(X)\in \mathbf {Q}[X]$ such that $f(\alpha )=0$ and algebraic integer if $f(X) \in \mathbf {Z}[X]$ such that f(X) is monic and $f(\alpha ) =0$. In fact $\alpha$ satisfies the unique polynomial P(X) of minimal degree with relatively prime integer coefficients such that the leading coefficient of P is positive.