Fermat near misses and the integral Hilbert Property

Paper

Abstract

We consider the Diophantine equation

for

, which is related to near misses for the quartic case of Fermat's Last Theorem. For certain

we show that the set of solutions is infinite, or more generally not thin. Our approach is via the geometry of del Pezzo surfaces of degree

, and we prove a more general result on non-thinness of integral points on double conic bundle surfaces.