Geodesic
Differences between Perfect Powers
Canadian mathematical bulletin, Tome 51 (2008) no. 3, pp. 337-347

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DOI

We apply the hypergeometric method of Thue and Siegel to prove that if $a$ and $b$ are positive integers, then the inequality $0\,<\,\left| {{a}^{x}}\,-\,{{b}^{y}} \right|\,<\,\frac{1}{4}\,\max \{{{a}^{x/2}},\,{{b}^{y/2}}\}$ has at most a single solution in positive integers $x$ and $y$ . This essentially sharpens a classic result of LeVeque.
DOI : 10.4153/CMB-2008-034-8
Mots-clés : 11D61, 11D45 
Bennett, Michael A. Differences between Perfect Powers. Canadian mathematical bulletin, Tome 51 (2008) no. 3, pp. 337-347. doi: 10.4153/CMB-2008-034-8
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     author = {Bennett, Michael A.},
     title = {Differences between {Perfect} {Powers}},
     journal = {Canadian mathematical bulletin},
     pages = {337--347},
     year = {2008},
     volume = {51},
     number = {3},
     doi = {10.4153/CMB-2008-034-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-034-8/}
}
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