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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5 papers · 2 filters

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★ 4 cited

On the Diophantine equation $\sum_{j = 1}^{k} j F_{j}^{p} = F_{n}^{q}$

Gökhan Soydan, László Németh, László Szalay

Let $F_{n}$ denote the $n^{t h}$ term of the Fibonacci sequence. In this paper, we investigate the Diophantine equation $F_{1}^{p} + 2 F_{2}^{p} + \dots + k F_{k}^{p} = F_{n}^{q}$ in the positive integers…

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.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

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

On the Diophantine equation ∑j=1k​jFjp​=Fnq​

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

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

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

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

On the Diophantine equation $\sum_{j = 1}^{k} j F_{j}^{p} = F_{n}^{q}$

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

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