Open AccessOn the extensibility of Diophantine triples {k-1, k+1, 4k} for Gaussian integers
Author(s) -
Zrinka Franušić
Publication year - 2008
Publication title -
glasnik matematički
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.332
H-Index - 17
eISSN - 1846-7989
pISSN - 0017-095X
DOI - 10.3336/gm.43.2.04
Subject(s) - extensibility , diophantine equation , mathematics , gaussian integer , discrete mathematics , arithmetic , computer science , programming language
In this paper, we prove that if {k-1, k+1, 4k, d}, where k Z[i] {0, ± 1}, d Z[i], is a Diophantine quadruple in Z[i], i.e. if (k-1)d+1, (k+1)d+1, 4kd+1 are perfect squares in Z[i], then d = 16k3-4k