Gökhan Soydan

most citedOn the Diophantine equation

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

13 citations · 15 across the 3 of their papers we have counts for

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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.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…

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

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

On the conjecture of Jeśmanowicz

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

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