Integral points on symmetric affine cubic surfaces

Abstract

We show that if $f(u)\in \mathbb{Z}[u]$ is a monic cubic polynomial, then for all but finitely many $n\in \mathbb{Z}$ the affine cubic surface $f(u_1)+f(u_2)+f(u_3)=n\subset {\mathbb{A}}_{\mathbb{Z}}^3$ has no integral Brauer-Manin obstruction to the Hasse principle.

References in corpus (1)

• Rational points of bounded height on general conic bundle surfaces

Cited by in corpus (1)

• Local-global principles for semi-integral points on Markoff orbifold pairs