Gökhan Soydan

most citedOn the Diophantine equation

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

13 citations · 17 across the 3 of their papers we have counts for

collaborators

3 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★ 2 cited

On the conjecture of Jeśmanowicz

Gökhan Soydan, Musa Demirci, Ismail Naci Cangul +1

We give a survey on some results covering the last 60 years concerning Jeśmanowicz' conjecture. Moreover, we conclude the survey with a new result by showing that the special Dioph…

math.NT2017★ 2 cited

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

Gökhan Soydan

Let $k, l \geq 2$ be fixed integers. In this paper, firstly, we prove that all solutions of the equation $(x + 1)^{k} + (x + 2)^{k} + ... + (l x)^{k} = y^{n}$ in integers $x, y, n$ with $x,y\geq1, n…

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

On the conjecture of Jeśmanowicz

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

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

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