Random Thue and Fermat equations
Volume 167 / 2015
Acta Arithmetica 167 (2015), 189-200
MSC: Primary 11D45; Secondary 11D41, 11E76, 11G35, 11G50, 14G05.
DOI: 10.4064/aa167-2-6
Abstract
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.
