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

Showing 2023Show all

2 papers · 1 filter

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…

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

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