Journal of Integer Sequences, Vol. 13 (2010), Article 10.9.6

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


Zrinka Franušić
Department of Mathematics
University of Zagreb
Bijenička cesta 30
10000 Zagreb
Croatia

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 ≠ -2.

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(Concerned with sequences A011922 A030063 A045899 A051048.)

Received August 19 2010; revised version received August 31 2010; November 17 2010. Published in Journal of Integer Sequences, December 7 2010.

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