Mirela Jukić Bokun
Assistant Professor Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR31000, Croatia¸

Research Interests
 Number Theory (Elliptic Curves, Diophantine Equations)
Degrees
 PhD in Mathematics, Department of Mathematics, University of Zagreb, 2011.
 MSc in Mathematics, Department of Mathematics, University of Zagreb, Croatia, 2008.
 BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2001.
Publications
 M. Jukić Bokun, I. Soldo, Pellian equations of special type, Mathematica Slovaca (2021), prihvaćen za objavljivanjeIn this paper, we consider the solvability of the Pellian equation x^2(d^2+1)y^2=m, in cases d=n^k, m=n^{2l1}, where k,l are positive integers, n is a composite positive integer and d=pq, m=pq^2, p,q are primes. We use the obtained results to prove results on the extendibility of some D(1)pairs to quadruples in the ring Z[sqrt{t}], with t>0.
 A. Filipin, M. Jukić Bokun, I. Soldo, On $D(1)$triples ${1,4p^2+1,1p}$ in the ring $Z[sqrt{p}]$ with a prime $p$, Periodica Mathematica Hungarica (2020), prihvaćen za objavljivanjeLet $p$ be a prime such that $4p^2+1$ is also a prime. In this paper, we prove that the $D(1)$set ${1,4p^2+1,1p}$ 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 $Z[sqrt{p}]$.
 A. Dujella, M. Jukić Bokun, I. Soldo, A Pellian equation with primes and applications to D(−1)quadruples, Bulletin of the Malaysian Mathematical Sciences Society 42 (2019), 29152926In this paper, we prove that the equation x^2 − (p^(2k+2) + 1)y^2 = −p^(2l+1), l∈{0, 1, . . . , k}, k ≥ 0, where p is an odd prime number, is not solvable in positive integers x and y. By combining that result with other known results on the existence of Diophantine quadruples, we are able to prove results on the extensibility of some D(−1)pairs to quadruples in the ring Z[√−t], t > 0.
 M. Jukić Bokun, I. Soldo, On the extensibility of D(1)pairs containing Fermat primes, Acta Mathematica Hungarica 159 (2019), 89108In this paper, we study the extendibility of a D(1)pair {1,p}, where p is a Fermat prime, to a D(1)quadruple in Z[sqrt{t}], t>0.
 A. Dujella, M. Jukić Bokun, I. Soldo, On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields, RACSAM 111 (2017), 11771185The possible torsion groups of elliptic curves induced by Diophan tine triples over quadratic fields, which do not appear over Q, are Z/2Z × Z/10Z, Z/2Z × Z/12Z and Z/4Z × Z/4Z. In this paper, we show that all these torsion groups indeed appear over some quadratic field. Moreover, we prove that there are infinitely many Diophantine triples over quadratic fields which induce elliptic curves with these tor sion groups.
 J. Aguirre, A. Dujella, M. Jukić Bokun, J.C. Peral, High rank elliptic curves with prescribed torsion group over quadratic fields, Periodica Mathematica Hungarica 68 (2014), 222230There are 26 possibilities for the torsion group of elliptic curves defined over quadratic number fields. We present examples of high rank elliptic curves with given torsion group which give the current records for most of the torsion groups. In particular, we show that for each possible torsion group, except maybe for Z/15Z, there exist an elliptic curve over some quadratic field with this torsion group and with rank >= 2.
 M. Jukić Bokun, Elliptic curves over quadratic fields with fixed torsion subgroup and positive rank, Glasnik Matematički 47 (2012), 277284For each of the torsion groups Z/2ZxZ/10Z, Z/2ZxZ/12Z, Z/15Z we find the quadratic field with the smallest absolute value of its discriminant such that there exists an elliptic curve with that torsion and positive rank. For the torsion groups Z/11Z, Z/14Z we solve the analogous problem after assuming the Parity conjecture.
 M. Jukić Bokun, On the rank of elliptic curves over Q(sqrt{3}) with torsion groups Z/3Z x Z/3Z and Z/3Z x Z/6Z, Proceedings of the Japan Academy. Series A Mathematical sciences 87/5 (2011), 6164We construct elliptic curves over the field Q(sqrt{3}) with torsion group Z/3Z x Z/3Z and ranks equal to 7 and an elliptic curve over the same field with torsion group Z/3Z x Z/6Z and rank equal to 6.
 A. Dujella, M. Jukić Bokun, On the rank of elliptic curves over Q(i) with torsion group Z/4Z × Z/4Z, Proceedings of the Japan Academy. Series A Mathematical sciences 86/6 (2010), 9396We construct an elliptic curve over Q(i) with torsion group Z/4Z * Z/4Z and rank equal to 7 and a family of elliptic curves with the same torsion group and rank >= 2.
 M. Jukić Bokun, A. Behin, Eulerova funkcija, Math.e : hrvatski matematički elektronski časopis 31 (2017)
 M. Đumić, M. Jukić Bokun, Euklidov algoritam, Osječki matematički list 13 (2013), 121137
 M. Duk, M. Jukić Bokun, L'Hospitalovo pravilo, Poučak 51 (2012), 1931
 M. Jukić, Apolonijev problem, Osječki matematički list 2/2 (2002), 8190
 M. Jukić, Broj e, Osječki matematički list 1/2 (2001), 7985
Projects
 GAMebased learning in MAthematics (GAMMA)
Coordinator of the project. Erasmus+ project (Key action: KA2  Cooperation for innovation and the exchange of good practices, Action Type: KA201: Strategic Partnership for school education).
 Diophantine mtuples, elliptic curves, Thue and index form equations
Project leader: prof. dr. Andrej Dujella, Department of Mathematics, University of Zagreb. Project by the Croatian Science Foundation for period 2014.2018.
 Passive control of mechanical models
Project leader: prof. dr. Ninoslav Truhar, Department of Mathematics, University of Osijek. Scientific project No.23523528181042 of the Croatian Ministry of Science, Education and Sports for the period 2007.2013. (junior researcher)
 Statistical aspects of parameter identification problems
Project leader: prof. dr. Mirta Benšić, Department of Mathematics, University of Osijek. Scientific project No. 0235002 of the Croatian Ministry of Science, Education and Sports for the period 2002.2006. (junior researcher)
Professional Activities
Editorial Boards Since 2012. technical editor of the international journal Mathematical Communications
Committee Memberships
Refereeing/Reviewing
Refereeing:
 Osječki matematički list
Workshops and Conferences
with talk:
 Elliptic curves over quadratic fields with fixed torsion subgroup and positive rank, 5th Croatian Mathematical Congress, Rijeka, Croatia, June 18  21, 2012
 High rank elliptic curves with prescribed torsion group over quadratic fields, Workshop on Number Theory and Algebra, Department of Mathematics, University of Zagreb, Zagreb, Croatia, November 2628, 2014
 On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields, 1st Croatian Combinatorial Days, Zagreb, Croatia, September 2930, 2016
 On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields, XXXth Journées Arithmétiques, Caen, France, July 37, 2017
 A Pellian equation with primes and its applications, Fibonacci Conference, Sarajevo, Bosna i Hercegovina, July 2123 2020.
 On the extensibility of some parametric families of D(1)pairs to quadruples in the ring Z[\sqrt{;t};], t>0, 9th International Eurasian Conference on Mathematical Sciences and Applications, Skopje, North Macedonia, August 2528, 2020.
without talk:
 Winter School on Explicit Methods in Number Theory, Debrecen, Hungary, January 2630, 2009
Seminar Talks
 Mestre's polynomial method for constructing elliptic curves of large rank, March 29, 2006, Seminar on Number Theory and Algebra, Department of Mathematics, University of Zagreb
 Some methods for constructing elliptic curves of large rank, April 2, 2008, Seminar on Number Theory and Algebra, Department of Mathematics, University of Zagreb
 Elliptic curves with nontrivilal torsion group and large rank, April 16, 2008, Seminar on Number Theory and Algebra, Department of Mathematics, University of Zagreb
 Elliptic curves of large rank over quadratic fields I, February 2, 2011, Seminar on Number Theory and Algebra, Department of Mathematics, University of Zagreb
 Elliptic curves of large rank over quadratic fields II, May 25, 2011, Seminar on Number Theory and Algebra, Department of Mathematics, University of Zagreb
Service Activities
Teaching
Konzultacije (Office Hours): Po dogovoru.
Prijedlog tema za diplomske i završne radove
Nastava u ovoj akademskoj godini
Financijska i aktuarska matematika
Primijenjena matematika za računalnu znanost
Nastavne aktivnosti u prošlosti (Past Courses)
Metodika nastave matematike II, Analitička geometrija, Algebra, Integralni račun, Obične diferencijalne jednadžbe, Geometrija prostora i ravnine, Elementarna matematika I, Elementarna matematika II, Linearna algebra I, Linearna algebra II, Linearna algebra III (Odjel za matematiku)
Matematika (Ekonomski fakultet)
Matematika III, Matematička analiza II, Linearna algebra (Elektrotehnički fakultet)
Matematika (Poljoprivredni fakultet)
Personal
2123 July 2020