The Catalan equation over function fields
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- by Joseph H. Silverman
- Trans. Amer. Math. Soc. 273 (1982), 201-205
- DOI: https://doi.org/10.1090/S0002-9947-1982-0664038-5
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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 $x,y \in K$.References
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Bibliographic Information
- © Copyright 1982 American Mathematical Society
- 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