Glasnik matematički, Vol. 43 No. 2, 2008.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.43.2.04
On the extensibility of Diophantine triples {k-1, k+1, 4k} for Gaussian integers
Zrinka Franušić
orcid.org/0000-0003-3481-8057
; Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
Sažetak
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.
Ključne riječi
Diophantine quadruples; simultaneous Diophantine equations; linear recurrence sequences
Hrčak ID:
28896
URI
Datum izdavanja:
10.11.2008.
Posjeta: 1.022 *