4 citations · 4 across the 5 of their papers we have counts for
8 papers
Perfect powers in sequences of polygonal numbers
Andrzej Dąbrowski, Salah Eddine Rihane, Gökhan Soydan +1
Let denote the -th -gonal number. Consider the Diophantine equation for integers and . All solutions to this equation are known f…
Genus two curves with everywhere good reduction over quadratic fields
Andrzej Dabrowski, Mohammad Sadek
We address the question of existence of absolutely simple abelian varieties of dimension 2 with everywhere good reduction over quadratic fields. The emphasis will be given to the c…
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…
Genus 2 curves with bad reduction at one odd prime
Andrzej Dabrowski, Mohammad Sadek
In this article we consider smooth projective curves of genus two described by integral equations of the form , where is monic of degree .…
On oracle factoring of integers
Andrzej Dąbrowski, Jacek Pomykała, Igor E. Shparlinski
We present an oracle factorisation algorithm which finds a nontrivial factor of almost all positive integers based on the knowledge of the number of points on certain elliptic…
Orders of Tate-Shafarevich groups for the cubic twists of
Andrzej Dąbrowski, Lucjan Szymaszkiewicz
This paper continues the authors previous investigations concerning orders of Tate-Shafarevich groups in quadratic twists of a given elliptic curve, and for the family of the Neuma…
Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves
Andrzej Dąbrowski, Lucjan Szymaszkiewicz
We present the results of our search for the orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves.
Behaviour of the order of Tate-Shafarevich groups for the quadratic twists of elliptic curves
Andrzej Dąbrowski, Lucjan Szymaszkiewicz
We present the results of our search for the orders of Tate-Shafarevich groups for the quadratic twists of elliptic curves. We formulate a general conjecture, giving for a fixed el…