Another topic of this research group deals with finding various Diophantine sets. The ancient Greek mathematician Diophantus solved some intriguing mathematical problems, and attempts to improve such results have given rise to entirely new mathematical disciplines over the coming millennia and centuries. With the advent of computers, the number of interesting problems has increased significantly, and we have managed to solve some of them.
As part of the research on this topic, collaboration was established with two scientists from the University of Zagreb (with professor Matija Kazalić and academician Andrej Dujella) who focus more on algebra and number theory, while the members of our research group make their contribution through the prism of computer science.
We use the Croatian High-Performance Computing infrastructure for various calculations, which enables us to explore complex mathematical problems with greater accuracy and speed. Hence we are grateful to the Croatian Competence Centre for High-Performance Computing for their support as it allows our research to be efficient and productive.
Our research efforts were previously directed towards exploring the connections between Newton’s iterative method for calculating the square root of a natural number, as well as its generalisations such as Housholder’s methods, and their connections with continued fractions. Now, focusing on Diophantine sets, we use this knowledge as a foundation for further research and understanding of mathematical problems ahead of us.
This research not only deepens the understanding of Diophantine sets but also raises new questions in mathematics and computer science. Through collaboration and dedicated work, we hope for new discoveries that will enrich these scientific disciplines.
