Bursa Uludağ Üni̇versi̇tesi̇

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20072026

most citedObservation of a charged charmoniumlike structure in e+e- to pi+pi-J/psi at \sqrt{s}=4.26 GeV

919 citations

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12 papers · 1 filter

math.NT2026

Perfect powers in sequences of polygonal numbers

Andrzej Dąbrowski, Salah Eddine Rihane, Gökhan Soydan +1

Let $P_{s} (n)$ denote the $n$ -th $s$ -gonal number. Consider the Diophantine equation $P_{s} (n) = t^{m}$ for integers $n, s, t$ and $m > 2$ . All solutions to this equation are known f…

math.NT2022★ 1 cited

General Terms of All Almost Balancing Numbers of First and Second Type

Ahmet Tekcan, Alper Erdem

In this work, we determined the general terms of all almost balancing numbers of first and second type in terms of balancing numbers and conversely we determined the general terms…

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.NT2020★ 10 cited

A brief survey on the generalized Lebesgue-Ramanujan-Nagell equation

Maohua Le, Gökhan Soydan

The generalized Lebesgue-Ramanujan-Nagell equation is an important type of polynomial-exponential Diophantine equation in number theory. In this survey, the recent results and some…

math.NT2019★ 4 cited

The Diophantine Equation $(x + 1)^{k} + (x + 2)^{k} + \dots + (ℓ x)^{k} = y^{n}$ Revisited

Daniele Bartoli, Gökhan Soydan

Let $k, ℓ \geq 2$ be fixed integers and $C$ be an effectively computable constant depending only on $k$ and $ℓ$ . In this paper, we prove that all solutions of the equation $(x+1…

math.NT2019

Rational sequences on different models of elliptic curves

Gamze Savaş ÇELİK, Mohammad Sadek, Gökhan Soydan

Given a set $S$ of elements in a number field $k$ , we discuss the existence of planar algebraic curves over $k$ which possess rational points whose $x$ -coordinates are exactly the…