Hairong Bai

most citedDiophantine equations involving Euler function

1 citations · 1 across the 3 of their papers we have counts for

collaborators

4 papers

math.NT2022

Positive rational number of the form $φ (k m^{a}) / φ (l n^{b})$

Hongjian Li, Pingzhi Yuan, Hairong Bai

Let $k, l, a$ and $b$ be positive integers with $max {a, b} \geq 2$ . In this paper, we show that every positive rational number can be written as the form $φ (k m^{a}) / φ (l n^{b})$ ,…

math.NT2020

On some conjectures of exponential Diophantine equations

Hairong Bai

In this paper, we consider the exponential Diophantine equation $a^{x} + b^{y} = c^{z},$ where $a, b, c$ be relatively prime positive integers such that $a^{2}+b^{2}=c^{r}, r\in Z^{+},…

math.NT2020

On the exponential Diophantine equation $(n - 1)^{x} + (n + 2)^{y} = n^{z}$

Hairong Bai, Elif Kızıldere, Gökhan Soydan +1

Suppose that $n$ is a positive integer. In this paper, we show that the exponential Diophantine equation $(n - 1)^{x} + (n + 2)^{y} = n^{z}, n \geq 2, x y z \neq = 0$ has only the positive i…

math.NT2020★ 1 cited

Diophantine equations involving Euler function

Hairong Bai

In this paper, we show that the equation $φ (∣ x^{m} - y^{m} ∣) = ∣ x^{n} - y^{n} ∣$ has no nontrivial solutions in integers $x, y, m, n$ with $x y \neq = 0, m > 0, n > 0$ except for the solutions $(x,y,…

Positive rational number of the form φ(kma)/φ(lnb)

On some conjectures of exponential Diophantine equations

On the exponential Diophantine equation (n−1)x+(n+2)y=nz

Diophantine equations involving Euler function

Positive rational number of the form $φ (k m^{a}) / φ (l n^{b})$

On the exponential Diophantine equation $(n - 1)^{x} + (n + 2)^{y} = n^{z}$