On the existence of Diophantine quadruples in $Z[\sqrt(-2)]$

Abstract

By the work of Abu Muriefah, Al-Rashed, Dujella and the author, the problem of the existence of D./-quadruples in the ring ZOE p 2 has been solved, except for the cases D 24a C 2 C .12b C 6/ p 2; D 24a C 5 C .12b C 6/ p 2; D 48a C 44 C .24b C 12