Year: 2025
Type: article
Abstract: This paper shows that the equation in the title has no solutions in the positive integers if (i) $n$ has prime factor congruent to $3$ (modulo $4$); or (ii) $8|n$; or $8|n-1$. Case (i) follows from an elementary argument. Case (ii) follows from the previous works of E. Dofs and the second author. Case (iii) follows from a standard Brauer-Manin obstruction argument.
Authors: Nguyen Duy TAN, Nguyen Xuan THO
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4414516177