Pregled bibliografske jedinice broj: 640984
On the extensibility of D(-1)-triples {;1, b, c}; in the ring Z[√ -t], t > 0
On the extensibility of D(-1)-triples {;1, b, c}; in the ring Z[√ -t], t > 0 // Studia scientiarum mathematicarum Hungarica, 50 (2013), 3; 296-330 doi:10.1556/SScMath.50.2013.3.1244 (međunarodna recenzija, članak, znanstveni)
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Naslov
On the extensibility of D(-1)-triples {;1, b, c}; in the ring Z[√ -t], t > 0
Autori
Soldo, Ivan
Izvornik
Studia scientiarum mathematicarum Hungarica (0081-6906) 50
(2013), 3;
296-330
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Diophantine quadruples; quadratic field; simultaneous Pellian equations; linear form in logarithms
Sažetak
Let b = 2, 5, 10 or 17 and t > 0. We study the existence of D(-1)-quadruples of the form {;1, b, c, d}; in the ring Z[√ -t]. We prove that if {;1, b, c}; is a D(-1)-triple in Z[√ -t], then c is an integer. As a consequence of this result, we show that for t \not\in {;1, 4, 9, 16}; there does not exist a subset of Z[√ -t] of the form {;1, b, c, d}; with the property that the product of any two of its distinct elements diminished by 1 is a square of an element in Z[√ -t].
Izvorni jezik
Engleski
Znanstvena područja
Matematika
Citiraj ovu publikaciju:
Časopis indeksira:
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
