Pregled bibliografske jedinice broj: 1086237
On D(−1)-triples {;1,4p^2+1,1−p}; in the ring Z[√p] with a prime p
On D(−1)-triples {;1,4p^2+1,1−p}; in the ring Z[√p] with a prime p // Periodica mathematica Hungarica, 85 (2022), 2; 292-302 doi:10.1007/s10998-021-00435-5 (međunarodna recenzija, članak, znanstveni)
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Naslov
On D(−1)-triples {;1,4p^2+1,1−p}; in the ring Z[√p]
with
a prime p
(On D(−1)-triples {;1,4p^2+1,1−p}; in the ring Z[√p]
with a prime p)
Autori
Filipin, Alan ; Jukić Bokun, Mirela ; Soldo, Ivan
Izvornik
Periodica mathematica Hungarica (0031-5303) 85
(2022), 2;
292-302
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Diophantine tuples ; quadratic field ; simultaneous pellian equations, linear form in logarithms
(Diophantine tuples, quadratic field, simultaneous pellian equations, linear form in logarithms)
Sažetak
Let p be a prime such that \(4p^2+1\) is also a prime. In this paper, we prove that the \(D(-1)\)-set \(\ {;1, 4p^2+1, 1-p\};\) cannot be extended with the forth element d such that the product of any two distinct elements of the new set decreased by 1 is a square in the ring \({;{;\mathbb {;Z};};};[\sqrt{;-p};]\).
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
HRZZ-IP-2018-01-1313 - Diofantska geometrija i primjene (DIOPHANT) (Kazalicki, Matija, HRZZ - 2018-01) ( CroRIS)
Ustanove:
Građevinski fakultet, Zagreb,
Sveučilište u Osijeku, Odjel za matematiku
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
