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On the existence of Diophantine quadruples in $Z[\sqrt(-2)]$
- Source :
- Miskolc Mathematical Notes. 14:265
- Publication Year :
- 2013
- Publisher :
- Mathematical Notes, 2013.
-
Abstract
- By the work of Abu Muriefah, Al-Rashed, Dujella and the author, the problem of the existence of D(z)-quadruples in the ring Z[√ -2] has been solved, except for the cases z=24a+2+(12b+6)√ -2, z=24a+5+(12b+6)√ -2, z=48a+44+(24b+12)√ -2. In this paper, we present some new formulas for D(z)-quadruples in these remaining cases, involving some congruence conditions modulo 11 on integers a and b. We show the existence of D(z)-quadruple for significant proportion of the remaining three cases.
Details
- ISSN :
- 17872413 and 17872405
- Volume :
- 14
- Database :
- OpenAIRE
- Journal :
- Miskolc Mathematical Notes
- Accession number :
- edsair.doi...........0aa1cb70e1deae8c7f393e5b88ccbac5