Speaker
Andrej Dujella
Description
A set of $m$ distinct nonzero rationals $\{a_1, a_2, ... , a_m\}$ such that $a_ia_j + 1$ is a perfect square for all $1 \leq i < j \leq m$, is called a rational Diophantine $m$-tuple. If, in addition, $a_i^2 + 1$ is a perfect square for $1 \leq i \leq m$, then we say the $m$-tuple is strong. In this talk, we will describe a construction of infinite families of rational Diophantine sextuples containing a strong Diophantine pair. In particular, we will show that infinitely many rational Diophantine sextuples contain a strong Diophantine pair $\{30464/2223, 22815/5168\}$.
This is a joint work with Matija Kazalicki and Vinko Petričević.
Primary author
Co-authors
Matija Kazalicki
(University of Zagreb)
Vinko Petričević
(Josip Juraj Strossmayer University of Osijek,)
