Zobrazeno 1 - 5
of 5
pro vyhledávání: '"Miljen Mikić"'
Autor:
Miljen Mikić, Andrej Dujella
Publikováno v:
Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti
Issue 542=24
Issue 542=24
Rational Diophantine triples, i.e. rationals a,b,c with the property that ab+1, ac+1, bc+1 are perfect squares, are often used in construction of elliptic curves with high rank. In this paper, we consider the opposite problem and ask how small can be
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d8431e6680b112bdf52915cf528e9e31
Autor:
Filip Najman, Miljen Mikić
Publikováno v:
Glasnik matematički
Volume 50
Issue 2
Volume 50
Issue 2
We fi nd the number of elliptic curves with a cyclic isogeny of degree n over various number fields by studying the modular curves X_0(n). We show that for n=14, 15, 20, 21, 49 there exist infinitely many quartic fields K such that # Y0(n)(Q)≠ # Y0
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::96598f1d10e4d48013edc0240fee00b2
https://doi.org/10.3336/gm.50.2.05
https://doi.org/10.3336/gm.50.2.05
Autor:
Andrej Dujella, Miljen Mikić
Publikováno v:
Analele Universitatii "Ovidius" Constanta - Seria Matematica. 22:79-90
A D(4)-m-tuple is a set of m integers such that the product of any two of them increased by 4 is a perfect square. A problem of extendibility of D(4)-m-tuples is closely connected with the properties of elliptic curves associated with them. In this p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7875a6b0f4e8ba4e137d411578ca6b4f
https://doi.org/10.2478/auom-2014-0033
https://doi.org/10.2478/auom-2014-0033
A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9a561163dfb3e83f434ab5347b53bc0d
Autor:
Miljen Mikić
Publikováno v:
Rocky Mountain J. Math. 45, no. 5 (2015), 1565-1589
The problem of the extendibility of Diophantine triples is closely connected with the Mordell-Weil group of the associated elliptic curve. In this paper, we examine Diophantine triples $\{k-1,k+1,c_l(k)\}$ and prove that the torsion group of the asso
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1e19a8f530dc5dfa8d81aa350e8ead81
https://www.bib.irb.hr/796419
https://www.bib.irb.hr/796419