On the extension of the Diophantine pair $\{1,3\}$ in $\Bbb Z[\sqrt d]$
J. Integer Seq. 13(9), Article 10.9.6, 11 p., electronic only (2010)
Summary
Summary: In this paper, we consider Diophantine triples of the form ${1,3,c}$ in the ring $Z[\sqrt d]$. We prove that the Diophantine pair ${1,3}$ cannot be extended to the Diophantine quintuple in $Z[\sqrt d]$ with $d < 0$ and $d \ne -2$.
