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

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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…

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

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 $g cd (a, b) > 1$