G. Soydan

most citedOn the Diophantine equation

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

13 citations · 18 across the 4 of their papers we have counts for

collaborators

5 papers

math.NT2017★ 13 cited

On the Diophantine equation $(x + 1)^{k} + (x + 2)^{k} + ... + (2 x)^{k} = y^{n}$

Attila Bérczes, István Pink, Gamze SavaŞ +1

In this work, we give upper bounds for $n$ on the title equation. Our results depend on assertions describing the precise exponents of $2$ and $3$ appearing in the prime factorizat…

math.NT2017

A note on the Diophantine equations $x^{2} \pm 5^{α} \cdot p^{n} = y^{n}$

Gökhan Soydan

Suppose that $x$ is odd, $n \geq 7$ and $p \in / {2, 5}$ are primes. In this paper, we prove that the Diophantine equations $x^{2} \pm 5^{α} p^{n} = y^{n}$ have no solutions in positive int…

math.NT2017

Complete solution of the Diophantine Equation $x^{2} + 5^{a} \cdot 1 1^{b} = y^{n}$

Gökhan Soydan, Nikos Tzanakis

The title equation is completely solved in integers $(n, x, y, a, b)$ , where $n \geq 3$ , $g cd (x, y) = 1$ and $a, b \geq 0$ . The most difficult stage of the resolution is the explicit resolu…

math.NT2011

The Group Structure of Bachet Elliptic Curves over Finite Fields F_{p}

Nazli Yildiz Ikikardes, Musa Demirci, Gokhan Soydan +1

Bachet elliptic curves are the curves y^2=x^3+a^3 and in this work the group structure E(F_{p}) of these curves over finite fields F_{p} is considered. It is shown that there are t…

math.NT2011★ 5 cited

Rational Points on Elliptic Curves y^2=x^3+a^3 in f_{p} where p{\equiv}1(mod6) is Prime

Musa Demirci, Gokhan Soydan, Ismail Naci Cangul

In this work, we consider the rational points on elliptic curves over finite fields F_{p}. We give results concerning the number of points on the elliptic curve y^2{\equiv}x^3+a^3(…

On the Diophantine equation (x+1)k+(x+2)k+...+(2x)k=yn

A note on the Diophantine equations x2±5α⋅pn=yn

Complete solution of the Diophantine Equation x2+5a⋅11b=yn

The Group Structure of Bachet Elliptic Curves over Finite Fields F_{p}

Rational Points on Elliptic Curves y^2=x^3+a^3 in f_{p} where p{\equiv}1(mod6) is Prime

On the Diophantine equation $(x + 1)^{k} + (x + 2)^{k} + ... + (2 x)^{k} = y^{n}$

A note on the Diophantine equations $x^{2} \pm 5^{α} \cdot p^{n} = y^{n}$

Complete solution of the Diophantine Equation $x^{2} + 5^{a} \cdot 1 1^{b} = y^{n}$