G. Soydan

activity

20102023

(x + 1)^{k} + (x + 2)^{k} + ... + (2 x)^{k} = y^{n}

13 citations · 50 across the 23 of their papers we have counts for

collaborators

28 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.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…

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.NT2021★ 3 cited

On elliptic curves induced by rational Diophantine quadruples

Andrej Dujella, Gökhan Soydan

In this paper, we consider elliptic curves induced by rational Diophantine quadruples, i.e. sets of four nonzero rationals such that the product of any two of them plus 1 is a perf…

math.NT2021

On a class of generalized Fermat equations of signature $(2, 2 n, 3)$

Karolina Chałupka, Andrzej Dąbrowski, Gökhan Soydan

We consider the Diophantine equation $7 x^{2} + y^{2 n} = 4 z^{3}$ . We determine all solutions to this equation for $n = 2, 3, 4$ and $5$ . We formulate a Kraus type criterion for show…

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

A modular approach to the generalized Ramanujan-Nagell equation

The Shuffle Variant of a Diophantine equation of Miyazaki and Togbé

On elliptic curves induced by rational Diophantine quadruples

On a class of generalized Fermat equations of signature (2,2n,3)

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

On a class of generalized Fermat equations of signature $(2, 2 n, 3)$