Year: 2025
Type: article
Abstract: In this paper, we provide a complete classification of the integer solutions to the Diophantine equation $x^2 + 3^a 19^b 73^c = \lambda y^n,$ where \( \lambda = 2^{\delta} \), \( x, y \geq 1 \), \( a, b, c, \delta \geq 0 \), \( n \geq 3 \), \( \gcd(x, y) = 1 \). Our approach combines the Primitive Divisor Theorem for Lehmer sequences, proved by Bilu, Hanrot, and Voutier, with fundamental properties of algebraic integer rings. By employing these methods, we determine all possible solutions in non-negative integers.
Authors: Murat Alan, Mustafa Aydın
Institution: Yıldız Technical University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414426985