1Department of Mathematics Royal Holloway, University of London Egham TW20 0EX, UK 2Mathematisches Institut Georg-August-Universität Göttingen Bunsenstr. 3-5 37073 Göttingen, Germany
Acta Arithmetica, Tome 167 (2015) no. 2, pp. 189-200
We consider Thue equations of the form $ax^k+by^k = 1$, and assuming the truth of the $abc$-conjecture, we show that almost all locally soluble Thue equations of degree at least three violate the Hasse principle. A similar conclusion holds true for Fermat equations $ax^k+by^k+cz^k = 0$ of degree at least six.
Keywords:
consider thue equations form assuming truth abc conjecture almost locally soluble thue equations degree least three violate hasse principle similar conclusion holds fermat equations degree least six
Affiliations des auteurs :
Rainer Dietmann
1
;
Oscar Marmon
2
1
Department of Mathematics Royal Holloway, University of London Egham TW20 0EX, UK
2
Mathematisches Institut Georg-August-Universität Göttingen Bunsenstr. 3-5 37073 Göttingen, Germany
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author = {Rainer Dietmann and Oscar Marmon},
title = {Random {Thue} and {Fermat} equations},
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Rainer Dietmann; Oscar Marmon. Random Thue and Fermat equations. Acta Arithmetica, Tome 167 (2015) no. 2, pp. 189-200. doi: 10.4064/aa167-2-6
