Differences between Perfect Powers

Canadian mathematical bulletin

关键词: Nevanlinna theory;    deficiency;    Riemann zeta function;   

DOI  :  10.4153/CMB-2008-034-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We apply the hypergeometric method of Thue and Siegel to provethat if $a$ and $b$ are positive integers, then the inequality $0 <| a^x - b^y | < frac{1}{4} , max { a^{x/2}, b^{y/2} }$has at most a single solution in positive integers $x$ and $y$.This essentially sharpens a classic result of LeVeque.

【 授权许可】

Unknown