R. Styer

activity

20112024

most citedA Survey on the Ternary Purely Exponential Diophantine Equation

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

8 citations · 8 across the 10 of their papers we have counts for

collaborators

11 papers

math.NT2024

At most one solution to $a^{x} + b^{y} = c^{z}$ for some ranges of $a$ , $b$ , $c$

Robert Styer

We consider the number of solutions in positive integers $(x, y, z)$ for the purely exponential Diophantine equation $a^{x} + b^{y} = c^{z}$ (with $g cd (a, b) = 1$ ). Apart from a list of known e…

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 >…

At most one solution to ax+by=cz for some ranges of a, b, c

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

At most one solution to $a^{x} + b^{y} = c^{z}$ for some ranges of $a$ , $b$ , $c$

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