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

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6 papers · 1 filter

math.NT2020

Rational Points in Geometric Progression on the Unit Circle

Gamze Savaş Çelik, Mohammad Sadek, Gökhan Soydan

A sequence of rational points on an algebraic planar curve is said to form an $r$ -geometric progression sequence if either the abscissae or the ordinates of these points form a geo…

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)^…

math.NT2020

Resolution of the equation $(3^{x_{1}} - 1) (3^{x_{2}} - 1) = (5^{y_{1}} - 1) (5^{y_{2}} - 1)$

Kálmán Liptai, László Németh, Gökhan Soydan +1

Consider the diophantine equation $(3^{x_{1}} - 1) (3^{x_{2}} - 1) = (5^{y_{1}} - 1) (5^{y_{2}} - 1)$ in positive integers $x_{1} \leq x_{2}$ , and $y_{1} \leq y_{2}$ . Each side of the equation is a product of two…

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.NT2020

On a class of Lebesgue-Ljunggren-Nagell type equations

Andrzej Dąbrowski, Nursena Günhan, Gökhan Soydan

Given odd, coprime integers $a$ , $b$ ( $a > 0$ ), we consider the Diophantine equation $a x^{2} + b^{2 l} = 4 y^{n}$ , $x, y \in Z$ , $l \in N$ , $n$ odd prime, $g cd (x, y) = 1$ . We completely…

Rational Points in Geometric Progression on the Unit Circle

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

Resolution of the equation (3x1​−1)(3x2​−1)=(5y1​−1)(5y2​−1)

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

On a class of Lebesgue-Ljunggren-Nagell type equations

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

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

Resolution of the equation $(3^{x_{1}} - 1) (3^{x_{2}} - 1) = (5^{y_{1}} - 1) (5^{y_{2}} - 1)$