Year: 2026
Type: preprint
Abstract: We consider the Diophantine equation \[ X^2+p^m=p_1^{n_1}p_2^{n_2}, \] where $p,p_1,p_2$ are distinct odd primes. Using factorizations in quadratic fields, sharp bounds for linear forms in two $p$-adic logarithms, elementary methods, and known results on exponential Diophantine equations, we obtain explicit bounds for $m,n_1,n_2$, and consequently the finiteness of the number of solutions for fixed $p,p_1,p_2$.
Source: arXiv (Cornell University)
Author: Ghadermarzi, Amir
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222512387