R. Scott

collaborators

2 papers

math.NT2026

Handling some Diophantine equation via Euclidean algorithm and its application to purely exponential equations

Takafumi Miyazaki, Reese Scott, Robert Styer

In this paper, we use a variety of classical and new research methods for ternary exponential Diophantine equations and extensive use of computer calculations to study the conjectu…

math.NT2024

Number of solutions to $a^{x} + b^{y} = c^{z}$ with $g cd (a, b) > 1$

Reese Scott, Robert Styer

We show that there are at most two solutions in positive integers $(x, y, z)$ to the equation $a^{x} + b^{y} = c^{z}$ for positive integers $a$ , $b$ , and $c$ all greater than one, with just on…

Handling some Diophantine equation via Euclidean algorithm and its application to purely exponential equations

Number of solutions to ax+by=cz with gcd(a,b)>1

Number of solutions to $a^{x} + b^{y} = c^{z}$ with $g cd (a, b) > 1$