### Mirela Jukić Bokun

Josip Juraj Strossmayer University of Osijek

### 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, Extensions of D(-1)-pairs in some imaginary quadratic fields, New York Journal of Mathematics (2024), prihvaćen za objavljivanjeIn this paper, we discuss the extensibility of Diophantine D(-1) pairs {a, b}, where a,b are positive integers in the ring Z[\sqrt{-k}], k>0. We prove that families of such D(-1)-pairs with b=p^i q^j, where p,q are different odd primes and i,j are positive integers cannot be extended to quadruples in certain rings Z[\sqrt{-k}], where k depends on p^i, q^i and a. Further, we present the result on non-existence of D(-1)-quintuples of a specific form in certain imaginary quadratic rings.
- A. Filipin, M. Jukić Bokun, I. Soldo, On $D(-1)$-triples ${1,4p^2+1,1-p}$ in the ring $Z[sqrt{-p}]$ with a prime $p$, Periodica Mathematica Hungarica
**85**(2022), 292-302Let $p$ 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 $Z[sqrt{-p}]$. - M. Jukić Bokun, I. Soldo, Pellian equations of special type, Mathematica Slovaca
**71**/6 (2021), 1599-1607In 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^{2l-1}, 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. 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), 2915-2926In 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), 89-108In 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), 1177-1185The 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), 222-230There 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), 277-284For 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), 61-64We 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), 93-96We 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.

- Lj. Jukić Matić, D. Marković, M. Jukić Bokun, Digital games and mathematics: Designing a game for learning probability in secondary school, 13th Congress of the European Society for Research in Mathematics Education, Budimpešta, 2023, 2973-2974

- Lj. Jukić Matić, M. Jukić Bokun, Game-based learning in mathematics: Handbook for teachers (2023)This handbook has been developed in the context of the European Erasmus+ project GAMMA (GAMe-based learning in MAthematics). The project aims to develop educational materials that will be useful for mathematics teachers who want to use game-based learning (GBL) founded on digital technology. The handbook provides background knowledge on (digital) game-based learning, but also examples and practical guidance for applications in mathematics education. More information about the project, learning materials and outputs can be found online on the project website: http://www.project-gamma.eu/.
- M. Jukić Bokun, Lj. Jukić Matić, D. Marković, Projekt GAMMA, Osječki matematički list
**22**/2 (2022), 161-170Projekt GAMMA je Erasmus+ projekt na kojemu je Odjel za matematiku Sveučilišta u Osijeku koordinator. U radu predstavljamo projekt i njegove rezultate, opisujemo aktivnosti važne za razvoj rezultata i najavljujemo službene diseminacijske aktivnosti. - 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), 121-137 - M. Duk, M. Jukić Bokun, L'Hospitalovo pravilo, Poučak
**51**(2012), 19-31 - M. Jukić, Apolonijev problem, Osječki matematički list
**2**/2 (2002), 81-90 - M. Jukić, Broj e, Osječki matematički list
**1**/2 (2001), 79-85

- M. Jukić Bokun, I. Soldo, Zbirka zadataka iz teorije brojeva, Fakultet primijenjene matematike i informatike, Osijek, 2023.

### Projects

*GAMe-based 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), 2020.-2023.

*Diophantine m-tuples, 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.235-2352818-1042 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

**Refereeing/Reviewing**

### Teaching

- Financijska i aktuarska matematika
- Primijenjena matematika za računalnu znanost
- Teorija brojeva
- Metodička matematička praksa II

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)

**Konzultacije (Office Hours):**Po dogovoru.

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