Alan Filipin (Zagreb): The extension of D(-k)-pair {k,k+1}

Austrian-Hungarian Diophantine Number Theory seminar
https://uni-salzburg.webex.com/uni-salzburg/j.php?MTID=mf70fce0a46969e4ded7c92853907c0bd

Abstract: In this talk we will consider the extension of D(-k)-pair {k,k+1} to a quadruple, where k is a positive integer. In the first part of the talk we will prove that if {k,k+1,c,d} is a D(-k)-quadruple with c<d, then c=1. In the second part we will consider the extension of D(-k)-triple {1,k,k+1} to a quadruple. We did not solve the problem completely for general k, but we will present some results when k is of special form, and we will give some conjectures that we believe are true. This is joint work with N. Adzaga and Y. Fujita.