Rational approximation to algebraic numbers of small height : the Diophantine equation j axn ÿ byn j

@inproceedings{BennettRationalAT,
title={Rational approximation to algebraic numbers of small height : the Diophantine equation j axn {\"y} byn j},
author={M. A. Bennett}
}

Following an approach originally due to Mahler and sharpened by Chudnovsky, we develop an explicit version of the multi-dimensional ``hypergeometric method'' for rational and algebraic approximation to algebraic numbers. Consequently, if a; b and n are given positive integers with nZ 3, we show that the equation of the title possesses at most one solution in positive integers x; y. Further results on Diophantine equations are also presented. The proofs are based upon explicit Pade… CONTINUE READING