Year: 2025
Type: article
Abstract: In this paper, we consider integer solutions (n,p,x,y,z) for the Diophantine equation n^x+(9p)^y=z^2 where n is positive, p is prime and x,y,z are non-negative. We show that this equation has no solution if n \equiv 1 \pmod{4} and p \equiv 1 \pmod{4}. Moreover, we find solutions of the Diophantine equation n^x+(9p)^y=z^2 in some cases.
Authors: Theerapon Buatong, Ronnason Chinram
Institution: Songkhla Rajabhat University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4412430228