M. Le

activity

20172021

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

10 citations · 11 across the 2 of their papers we have counts for

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math.NT2021

On the power values of the sum of three squares in arithmetic progression

Maohua Le, Gökhan Soydan

In this paper, using a deep result on the existence of primitive divisors of Lehmer numbers due to Y. Bilu, G. Hanrot and P. M. Voutier, we first give an explicit formula for all p…

math.NT2020

A note on the ternary purely exponential Diophantine equation $A^{x} + B^{y} = C^{z}$ with $A + B = C^{2}$

Elif Kızıldere, Maohua Le, Gökhan Soydan

Let $ℓ, m, r$ be fixed positive integers such that $2 ∤ ℓ$ , $3 ∤ ℓ m$ , $ℓ > r$ and $3 ∣ r$ . In this paper, using the BHV theorem on the existence of primitive div…

math.NT2020★ 10 cited

A brief survey on the generalized Lebesgue-Ramanujan-Nagell equation

Maohua Le, Gökhan Soydan

The generalized Lebesgue-Ramanujan-Nagell equation is an important type of polynomial-exponential Diophantine equation in number theory. In this survey, the recent results and some…

math.NT2018

An application of Baker's method to the Jeśmanowicz' conjecture on primitive Pythagorean triples

Maohua Le

Let $m$ , $n$ be positive integers such that $m > n$ , $g cd (m, n) = 1$ and $m \neq \equiv n mod 2$ . In 1956, L. Jeśmanowicz \cite{Jes} conjectured that the equation $(m^2 - n^2)^x + (2m…

math.NT2018

An application of the BHV theorem to a new conjecture on exponential diophantine equations

Maohua Le

Let $A$ , $B$ be fixed positive integers such that $min {A, B} > 1$ , $g cd (A, B) = 1$ and $A B \equiv 0 mod 2$ , and let $n$ be a positive integer with $n > 1$ . In this paper, using a…

math.NT2018

An Upper Bound for the Number of Solutions of Ternary Purely Exponential Diophantine Equations II

Yongzhong Hu, Maohua Le

Let $a, b, c$ be fixed coprime positive integers with $min {a, b, c} > 1$ . In this paper, by analyzing the gap rule for solutions of the ternary purely exponential diophantine equation…

On the power values of the sum of three squares in arithmetic progression

A note on the ternary purely exponential Diophantine equation Ax+By=Cz with A+B=C2

A brief survey on the generalized Lebesgue-Ramanujan-Nagell equation

An application of Baker's method to the Jeśmanowicz' conjecture on primitive Pythagorean triples

An application of the BHV theorem to a new conjecture on exponential diophantine equations

An Upper Bound for the Number of Solutions of Ternary Purely Exponential Diophantine Equations II

A note on the ternary purely exponential Diophantine equation $A^{x} + B^{y} = C^{z}$ with $A + B = C^{2}$