Parametric solutions to the generalized Fermat equation
In this paper we examine parametric solutions to the generalized Fermat equation, xp+yq=zr. Simple criteria are given for the existence of solutions over an algebraically closed field and all such solutions are described. Parametric solutions over non-algebraically closed fields are then considered,...
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Format: | Others |
Language: | en |
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McGill University
1999
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Online Access: | http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=21550 |
Summary: | In this paper we examine parametric solutions to the generalized Fermat equation, xp+yq=zr. Simple criteria are given for the existence of solutions over an algebraically closed field and all such solutions are described. Parametric solutions over non-algebraically closed fields are then considered, along with an investigation of the number of distinct classes of solutions, up to an appropriate notion of equivalence. |
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