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Random Thue and Fermat equations

Rainer Dietmann;  Oscar Marmon — 2015

Acta Arithmetica

We consider Thue equations of the form a x k + b y 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 a x k + b y k + c z k = 0 of degree at least six.

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