proof of Liouville approximation theorem

Let α satisfy the equation f(α)=anαn+an-1αn-1++a0=0 where the ai are integers. Choose M such that M>maxα-1xα+1|f(x)|.

Suppose pq lies in (α-1,α+1) and f(pq)0.


since the numerator is a non-zero integer.

Title proof of Liouville approximation theorem
Canonical name ProofOfLiouvilleApproximationTheorem
Date of creation 2013-03-22 13:19:22
Last modified on 2013-03-22 13:19:22
Owner lieven (1075)
Last modified by lieven (1075)
Numerical id 6
Author lieven (1075)
Entry type Proof
Classification msc 11J68