9 citations · 23 across the 38 of their papers we have counts for
4 papers · 2 filters
Some experiments with Ramanujan-Nagell type Diophantine equations
Maciej Ulas
Stiller proved that the Diophantine equation has exactly six solutions in positive integers. Motivated by this result we are interested in constructions of…
Some identities involving Prouhet-Thue-Morse sequence and its relatives
Jakub Byszewski, Maciej Ulas
Let denote the sum of digits of an integer in base . Motivated by certain identities of Nieto, and Bateman and Bradley involving sums of the form $\sum_{i=0}^{2^{…
Constructions of diagonal quartic and sextic surfaces with infinitely many rational points
Andrew Bremner, Ajai Choudhry, Maciej Ulas
In this note we construct several infinite families of diagonal quartic surfaces \begin{equation*} ax^4+by^4+cz^4+dw^4=0, \end{equation*} where with in…
Variations on twists of tuples of hyperelliptic curves and related results
Tomasz Jędrzejak, Maciej Ulas
Let $f\in\Q[x]$ be a square-free polynomial of degree and be an odd positive integer. Based on our earlier investigations we prove that there exists a function $…