R. Scott

activity

20062026

most citedA Survey on the Ternary Purely Exponential Diophantine Equation

a^{x} + b^{y} = c^{z}

8 citations · 9 across the 12 of their papers we have counts for

collaborators

13 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…

math.NT2022

On a conjecture concerning the number of solutions to $a^{x} + b^{y} = c^{z}$ , II

Maohua Le, Reese Scott, Robert Styer

Let $a$ , $b$ , $c$ be distinct primes with $a < b$ . Let $S (a, b, c)$ denote the number of positive integer solutions $(x, y, z)$ of the equation $a^{x} + b^{y} = c^{z}$ . In a previous paper \ci…

math.NT2022

On a conjecture concerning the number of solutions to $a^{x} + b^{y} = c^{z}$

Maohua Le, Reese Scott, Robert Styer

Let $a$ , $b$ , $c$ be fixed coprime positive integers with $min {a, b, c} > 1$ . Let $N (a, b, c)$ denote the number of positive integer solutions $(x, y, z)$ of the equation $a^x + b^y…

math.NT2022

Number of solutions to $a^{x} + b^{y} = c^{z}$ , A Shorter Version

Reese Scott, Robert Styer

For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$ , there are at most two solutions in positive integers $(x, y, z)$ to the equation $a^x + b^y = c^z…

math.NT2020

Two terms with known prime divisors adding to a power: REVISED with APPENDICES

Reese Scott, Robert Styer

Let $c$ be a positive odd integer and $R$ a set of $n$ primes coprime with $c$ . We consider equations $X + Y = c^{z}$ in three integer unknowns $X$ , $Y$ , $z$ , where $z > 0$ , $Y > X >…

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

On a conjecture concerning the number of solutions to ax+by=cz, II

On a conjecture concerning the number of solutions to ax+by=cz

Number of solutions to ax+by=cz, A Shorter Version

Two terms with known prime divisors adding to a power: REVISED with APPENDICES

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

On a conjecture concerning the number of solutions to $a^{x} + b^{y} = c^{z}$ , II

On a conjecture concerning the number of solutions to $a^{x} + b^{y} = c^{z}$

Number of solutions to $a^{x} + b^{y} = c^{z}$ , A Shorter Version