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

13 Jan 2020 · Adžaga Nikola, Filipin Alan, Fujita Yasutsugu ·

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 $d=1$.