Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4652160 | Electronic Notes in Discrete Mathematics | 2013 | 6 Pages |
Abstract
Let a,b and n be positive integers with n⩾3 and consider the binomial Thue inequality |axn−byn|⩽3. In this paper, we extend a result of the first author and prove that, apart from finitely many explicitly given exceptions, this inequality has at most a single solution in positive integers x and y. In the proof, we combine lower bounds for linear forms in logarithms of algebraic numbers with the hypergeometric method of Thue-Siegel and an assortment of techniques from computational Diophantine approximation.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics