LE Mao-hua

collaborators

3 papers

math.NT2023

On the Ternary Purely Exponential Diophantine Equation $(ak)^{x} + (bk)^{y} = ((a + b) k)^{z}$ with Prime Powers $a$ and $b$

Maohua Le, Gökhan Soydan

Let $k$ be a positive integer, and let $a, b$ be coprime positive integers with $min {a, b} > 1$ . In this paper, using a combination of some elementary number theory techniques with…

math.NT2023

An elementary approach to the generalized Ramanujan-Nagell equation

Elif Kızıldere Mutlu, Maohua Le, Gökhan Soydan

Let $k$ be a fixed positive integer with $k > 1$ . In this paper, using various elementary methods in number theory, we give criteria under which the equation $x^{2} + (2 k - 1)^{y} = k^{z}$ has n…

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…

On the Ternary Purely Exponential Diophantine Equation (ak)x+(bk)y=((a+b)k)z with Prime Powers a and b

An elementary approach to the generalized Ramanujan-Nagell equation

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

On the Ternary Purely Exponential Diophantine Equation $(ak)^{x} + (bk)^{y} = ((a + b) k)^{z}$ with Prime Powers $a$ and $b$

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