Pregled bibliografske jedinice broj: 773097
D(4)-pair {;a, b}; and its extension
D(4)-pair {;a, b}; and its extension // Workshop on Number Theory and Algebra
Zagreb, 2014. str. 1-1 (pozvano predavanje, nije recenziran, sažetak, znanstveni)
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Naslov
D(4)-pair {;a, b}; and its extension
Autori
Baćić, Ljubica ; Filipin, Alan
Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni
Izvornik
Workshop on Number Theory and Algebra
/ - Zagreb, 2014, 1-1
Skup
Workshop on Number Theory and Algebra on the occasion of 60th birthday of Ivica Gusić
Mjesto i datum
Zagreb, Hrvatska, 26.11.2014. - 28.11.2014
Vrsta sudjelovanja
Pozvano predavanje
Vrsta recenzije
Nije recenziran
Ključne riječi
Diophantine tuples; system of Diophantine equations
Sažetak
We consider the extensibility of a general D(4)-pair {;a, b}; and prove some results that support the conjecture that there does not exist a D(4)-quintuple. In the proof we use the standard methods used in solving similar problems. So we firstly transform our problem into solving the system of simultaneous pellian equations which furthermore leads to nding intersection of binary recurrence sequences. It is eventually solved combining congruence method with hypergeometric method and Baker's theory of linear forms in logarithms. Here we made Baker-Davenport reduction at the beginning and also improved Rickert's theorem in our special case.
Izvorni jezik
Engleski
