A. Dąbrowski

activity

20182026

collaborators

3 papers

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.NT2021

On a class of generalized Fermat equations of signature $(2, 2 n, 3)$

Karolina Chałupka, Andrzej Dąbrowski, Gökhan Soydan

We consider the Diophantine equation $7 x^{2} + y^{2 n} = 4 z^{3}$ . We determine all solutions to this equation for $n = 2, 3, 4$ and $5$ . We formulate a Kraus type criterion for show…

math.NT2018

Orders of Tate-Shafarevich groups for the cubic twists of $X_{0} (27)$

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…

Perfect powers in sequences of polygonal numbers

On a class of generalized Fermat equations of signature (2,2n,3)

Orders of Tate-Shafarevich groups for the cubic twists of X0​(27)

On a class of generalized Fermat equations of signature $(2, 2 n, 3)$

Orders of Tate-Shafarevich groups for the cubic twists of $X_{0} (27)$