  The objective of the paper is to determine the complete solutions for the
Diophantine equation $x^2 + 3^{\alpha}113^{\beta} = y^{\mathfrak{n}}$ in
positive integers $x$ and $y$ (where $x, y \geq 1$), non-negative exponents
$\alpha$ and $\beta$, and an integer $\mathfrak{n}\geq 3$, subject to the
condition $\text{gcd}(x, y) = 1$.
