Pregled bibliografske jedinice broj: 983388
Applications of a Diophantine equation of a special type
Applications of a Diophantine equation of a special type // Conference on Diophantine m-tuples and related problems II
Westville (NJ), Sjedinjene Američke Države, 2018. str. 8-8 (predavanje, nije recenziran, sažetak, znanstveni)
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Naslov
Applications of a Diophantine equation of a
special type
Autori
Soldo, Ivan
Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni
Izvornik
Conference on Diophantine m-tuples and related problems II
/ - , 2018, 8-8
Skup
Conference on Diophantine m-tuples and related problems II
Mjesto i datum
Westville (NJ), Sjedinjene Američke Države, 15.10.2018. - 17.10.2018
Vrsta sudjelovanja
Predavanje
Vrsta recenzije
Nije recenziran
Ključne riječi
Diophantine quadruples ; quadratic field ; Pellian equations ;
Sažetak
This is a joint work with Andrej Dujella and Mirela Jukic Bokun. Let p be an odd prime and k non-negative integer. We prove that the Pellian equation x^2 − (p^(2k+2) + 1)y^2 = −p^(2l+1), l ∈ {; ; ; 0, 1, . . . , k}; ; ; , is not solvable in positive integers x and y. By combining that result with other known results on the topic of Diophantine m-tuples, we obtain results on extensibility of D(−1)-pairs of the form {; ; ; 1, 2b}; ; ; , where 2b = p^(2j) + 1, j > 0, and p is an odd prime, to D(−1)-quadruples in the ring Z[√−t], t > 0.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
