Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/wiley/on-the-equations-zm-f-x-y-and-axp-byq-czr-TEPFBkDf04
References (8)
-
G. Faltings (1991)
Diophantine approximation on abelian varietiesAnnals of Mathematics, 133
-
Paul Vojta (1991)
Siegel's theorem in the compact caseAnnals of Mathematics, 133
-
N. Elkies (1991)
ABC implies MordellInternational Mathematics Research Notices, 1991
-
Paul Vojta (1987)
Diophantine Approximations and Value Distribution Theory -
K. Ribet (1990)
On modular representations of $$(\bar Q/Q)$$ arising from modular formsInventiones mathematicae, 100
-
P. Erdös, J. Selfridge (1975)
The product of consecutive integers is never a powerIllinois Journal of Mathematics, 19
-
E. Bombieri, E. Bombieri, J. Mueller, J. Mueller (1991)
The generalized fermat equation in function fieldsJournal of Number Theory, 39
-
L. Mordell (1969)
Diophantine equations
- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/27.6.513
- Publisher site
- See Article on Publisher Site
Abstract
We investigate integer solutions of the superelliptic equation (1)zm=F(x,y), where F is a homogeneous polynomial with integer coefficients, and of the generalized Fermat equation (2)Axp+Byq=Czr, where A, B and C are non‐zero integers. Call an integer solution (x, y, z) to such an equation proper if gcd(x, y, z) = 1. Using Faltings' Theorem, we shall give criteria for these equations to have only finitely many proper solutions.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Nov 1, 1995