Elif Kizildere

most citedOn the Diophantine equation

(5 p n^{2} - 1)^{x} + (p (p - 5) n^{2} + 1)^{y} = (p n)^{z}

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

collaborators

4 papers

math.NT2021

The Shuffle Variant of a Diophantine equation of Miyazaki and Togbé

Elif Kızıldere, Gökhan Soydan, Qing Han +1

In 2012, T. Miyazaki and A. Togbé gave all of the solutions of the Diophantine equations $(2 am - 1)^{x} + (2 m)^{y} = (2 am + 1)^{z}$ and $b^{x} + 2^{y} = (b + 2)^{z}$ in positive integers $x, y, z,$ $a > 1$ and…

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

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★ 2 cited

On the Diophantine equation $(5 p n^{2} - 1)^{x} + (p (p - 5) n^{2} + 1)^{y} = (p n)^{z}$

Elif Kızıldere, Gökhan Soydan

Let $p$ be a prime number with $p > 3$ , $p \equiv 3 (mod 4)$ and let $n$ be a positive integer. In this paper, we prove that the Diophantine equation $(5pn^{2}-1)^{x}+(p(p-5)n^{2}+1)^…

The Shuffle Variant of a Diophantine equation of Miyazaki and Togbé

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

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

On the Diophantine equation (5pn2−1)x+(p(p−5)n2+1)y=(pn)z

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

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

On the Diophantine equation $(5 p n^{2} - 1)^{x} + (p (p - 5) n^{2} + 1)^{y} = (p n)^{z}$