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ON A CLASS OF GENERALIZED FERMAT EQUATIONS

Part of: Arithmetic algebraic geometry Diophantine equations Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  18 June 2010

ANDRZEJ DĄBROWSKI
ANDRZEJ DĄBROWSKI*
Affiliation:
Institute of Mathematics, University of Szczecin, ul. Wielkopolska 15, 70-451 Szczecin, Poland (email: [email protected])
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Abstract

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We generalize the main result of the paper by Bennett and Mulholland [‘On the diophantine equation xn+yn=2αpz2’, C. R. Math. Acad. Sci. Soc. R. Can.28 (2006), 6–11] concerning the solubility of the diophantine equation xn+yn=2αpz2. We also demonstrate, by way of examples, that questions about solubility of a class of diophantine equations of type (3,3,p) or (4,2,p) can be reduced, in certain cases, to studying several equations of the type (p,p,2).

Keywords

generalized Fermat equationelliptic curvemodular formGalois representation

MSC classification

Secondary: 11D41: Higher degree equations; Fermat's equation 11F80: Galois representations 11G05: Elliptic curves over global fields
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 3 , December 2010 , pp. 505 - 510
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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