Research Article

Rational approximations to algebraic numbers

K. F. Rotha1

a1 University College, London

It was remarked by Liouville in 1844 that there is an obvious limit to the accuracy with which algebraic numbers can be approximated by rational numbers; if α is an algebraic number of degree n (at least 2) then


for all rational numbers h/q, where A is a positive number depending only on α.

(Received January 26 1955)

(Revised May 20 1955)