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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The Catalan equation over function fields


Author: Joseph H. Silverman
Journal: Trans. Amer. Math. Soc. 273 (1982), 201-205
MSC: Primary 10B15; Secondary 12A90
DOI: https://doi.org/10.1090/S0002-9947-1982-0664038-5
MathSciNet review: 664038
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Abstract: Let $ K$ be the function field of a projective variety. Fix $ a,b,c \in {K^ \ast }$. We show that if $ \max \{ m,n\} $ is sufficiently large, then the Catalan equation $ a{x^m} + b{y^n} = c$ has no nonconstant solutions $ x,y \in K$.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0664038-5
Article copyright: © Copyright 1982 American Mathematical Society