13 citations · 50 across the 23 of their papers we have counts for
5 papers · 1 filter
A modular approach to the generalized Ramanujan-Nagell equation
Elif Kızıldere Mutlu, Maohua Le, Gökhan Soydan
Let be a positive integer. In this paper, using the modular approach, we prove that if , and is an odd prime power, then under the GRH, t…
The Shuffle Variant of a Diophantine equation of Miyazaki and Togbé
Elif Kızıldere, Gökhan Soydan, Qing Han +1
In 2012, T. Miyazaki and A. Togbé gave all of the solutions of the Diophantine equations and in positive integers and…
On elliptic curves induced by rational Diophantine quadruples
Andrej Dujella, Gökhan Soydan
In this paper, we consider elliptic curves induced by rational Diophantine quadruples, i.e. sets of four nonzero rationals such that the product of any two of them plus 1 is a perf…
On a class of generalized Fermat equations of signature
Karolina Chałupka, Andrzej Dąbrowski, Gökhan Soydan
We consider the Diophantine equation . We determine all solutions to this equation for and . We formulate a Kraus type criterion for show…
On the power values of the sum of three squares in arithmetic progression
Maohua Le, Gökhan Soydan
In this paper, using a deep result on the existence of primitive divisors of Lehmer numbers due to Y. Bilu, G. Hanrot and P. M. Voutier, we first give an explicit formula for all p…