Geodesic
Random Thue and Fermat equations
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
Acta Arithmetica, Tome 167 (2015) no. 2, pp. 189-200 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa167-2-6
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

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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     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

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