# On the Extension of the Diophantine Pair { 1 , 3 } in Z [ √ d ]

• Zrinka Franušić
• Published 2010

#### Abstract

In this paper, we consider Diophantine triples of the form {1, 3, c} in the ring Z[ √ d]. We prove that the Diophantine pair {1, 3} cannot be extended to the Diophantine quintuple in Z[ √ d] with d < 0 and d 6= −2.

### Cite this paper

@inproceedings{Franui2010OnTE, title={On the Extension of the Diophantine Pair \{ 1 , 3 \} in Z [ √ d ]}, author={Zrinka Franu{\vs}i{\'c}}, year={2010} }