An Exponential Diophantine equation $x^2+3^α 113^β=y^{\mathfrak{n}}$
The objective of the paper is to determine the complete solutions for the Diophantine equation $x^2 + 3^α113^β = y^{\mathfrak{n}}$ in positive integers $x$ and $y$ (where $x, y \geq 1$), non-negative exponents $α$ and $β$, and an integer $\mathfrak{n}\geq 3$, subject to the condition $\text{gcd}(x, y) = 1$.
math.NT↗