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On the extensibility of Diophantine triples {; ; ; k-1, k+1, 4k}; ; ; for Gaussian integers (CROSBI ID 137727)
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Franušić, Zrinka
On the extensibility of Diophantine triples {; ; ; k-1, k+1, 4k}; ; ; for Gaussian integers // Glasnik matematički, 43 (2008), 2; 265-291. doi: 10.3336/gm.43.2.
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Franušić, Zrinka
engleski
On the extensibility of Diophantine triples {; ; ; k-1, k+1, 4k}; ; ; for Gaussian integers
In this paper, we prove that if {; ; k-1, k+1, 4k, d}; ; , where k in Z[i] \ {; ; 0, +-1}; ; , d in 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=16k^3-4k.
Diophantine quadruples; Simultaneous Diophantine equations; Linear recurrence sequences
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