Year: 2025
Type: preprint
Abstract: Let $a$ and $b$ be two distinct fixed positive integers such that $\min \{a,b\}>1.$ First, we correct an oversight from \cite{X-Z}. Then, we show that the equation in the title with $b \equiv 3 \pmod 8$, $b$ prime and $a$ even has no solution in positive integers $n, x$. This generalizes a result of Szalay \cite{L}.
Source: arXiv (Cornell University)
Authors: Noubissie, Armand, Togbe, Alain, Zhang, Zhongfeng
Institution: Zhaoqing University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2121754997, G5078310481
OpenAlex ID: W6979352093