Random Thue and Fermat equations

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Abstract

We consider Thue equations of the form axk+byk=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 axk+byk+czk=0 of degree at least six.
Original languageEnglish
Pages (from-to)189-200
Number of pages12
JournalActa Arithmetica
Volume167
DOIs
Publication statusPublished - 2015

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