M. Le

activity

20172023

most citedA brief survey on the generalized Lebesgue-Ramanujan-Nagell equation

10 citations · 23 across the 14 of their papers we have counts for

collaborators

14 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 $a^{x} + b^{y} = c^{z}$ , 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

A binary quadratic approach to $X^{2} + (2 k - 1)^{Y} = k^{Z}$

Maohua Le, Anitha Srinivasan

A conjecture of N. Terai states that for any integer $k > 1$ , the equation $x^{2} + (2 k - 1)^{y} = k^{z}$ has only one solution, namely, $(x, y, z) = (k - 1, 1, 2) .$ Using the structure of class…

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.NT2021

A modular approach to the generalized Ramanujan-Nagell equation

Elif Kızıldere Mutlu, Maohua Le, Gökhan Soydan

Let $k$ be a positive integer. In this paper, using the modular approach, we prove that if $k \equiv 0 (mod 4)$ , $30 < k < 724$ and $2 k - 1$ is an odd prime power, then under the GRH, t…

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, II

A binary quadratic approach to X2+(2k−1)Y=kZ

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

A modular approach to the generalized Ramanujan-Nagell equation

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 $a^{x} + b^{y} = c^{z}$ , II

A binary quadratic approach to $X^{2} + (2 k - 1)^{Y} = k^{Z}$

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