The extension of the $D(-k)$-pair $\{k,k+1\}$ to a quadruple

Nikola Adžaga, Alan Filipin, Yasutsugu Fujita

Let $k$ be a positive integer. In this paper, we prove that if $\{k,k+1,c,d\}$ is a $D(-k)$-quadruple with $c>1$, then $d=1$.