Opcije pristupačnosti Pristupačnost

Alan Filipin

O djelatniku

prof. dr. sc. Alan Filipin

Zvanje:
redoviti profesor u trajnom izboru
Kabinet:
soba 107, Kranjčevićeva 2
Konzultacije:

Četvrtkom od 10 do 12 sati

Telefon:
01/4690 838
Telefon kućni:
838
Zavod/služba:
Zavod za matematiku
Godina diplomiranja:
2001.
Godina magistriranja:
2004.
Godina doktoriranja:
2006.
Na zavodu od:
2004.

Nastava

prijediplomski

diplomski

Životopis

Osobne informacije:

  • Datum rođenja: 15.8.1977.
  • Mjesto rođenja: Zagreb

Školovanje i akademski stupnjevi:

  • 1984.-1992. Osnovna škola "Jabukovac", Zagreb
  • 1992.-1996. 15. Gimnazija, Zagreb
  • 1996.-2001. PMF - Matematički odjel Sveučilišta u Zagrebu, inženjerski profil, smjer teorijska matematika, diplomirao 6.7.2001. s radom "Eksponencijalne formule", voditelj rada prof.dr.sc. Dragutin Svrtan
  • 2002. Diplomirao i na profesorskom profilu, profesor matematike, PMF - Matematički odjel Sveučilišta u Zagrebu, 20.5.2002.
  • 2004. Magistrirao s radom "Primjena LLL-algoritma u rješavanju diofantskih jednadžbi", voditelj rada prof.dr.sc. Andrej Dujella,  na PMF - Matematički odjel Sveučilišta u Zagrebu, 13.7.2004.
  • 2006. Doktorirao s disertacijom "Sustavi pellovskih jednadžbi i problem proširenja nekih Diofantovih trojki", voditelj rada prof.dr.sc. Andrej Dujella, na PMF - Matematički odjel Sveučilišta u Zagrebu, 2.11.2006.

Ostalo:

  • od 1. veljače 2007. do 31. siječnja 2008. bio sam na poslijedoktorskom usavršavanju na TU Graz, Austrija

Objavljeni radovi u Hrvatskoj znanstvenoj bibliografiji

Fibonacci and Lucas numbers as products of three repdigits in base g

2024., Adedji, Kouessi Norbert ; Filipin, Alan ; Togbe, Alain

Rendiconti del Circolo Matematico di Palermo

On the D(4)-pairs {;a,ka}; with k ∈ {;2,3,6};

2023., Adedji, Kouessi Norbert ; Bliznac Trebješanin, Marija ; Filipin, Alan ; Togbe, Alain
clanak
Glasnik matematički

Triangular Diophantine tuples from {;1, 2};

2023., Filipin, Alan ; Szalay, Laszlo

Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti

Fibonacci or Lucas numbers which are concatenations of two g-repdigits

2023., Adedji, Kouessi Norbert ; Filipin, Alan ; Rihane, Salah Eddine ; Togbe, Alain

The Fibonacci quarterly

Polynomial D(-3)-quadruples

2022., Filipin, Alan ; Jurasić, Ana
sazetak
Number Theory Conference 2022 In honour of Professors Kálmán Győry, János Pintz and András Sárközy

Diofantovi skupovi

2022., Filipin, Alan ; Franušić, Zrinka

Products of two repdigits in some recurrence sequences

2022., Filipin, Alan ; Adedji, Kouessi Norbert ; Togbe, Alain
sazetak
The Twentieth International Conference on Fibonacci Numbers and Their Applications

On the existence of D(-3)-quadruples in Z[X]

2022., Filipin, Alan ; Jurasić, Ana
clanak
Glasnik matematički

On the extensions of the Diophantine triples in Gaussian integers

2022., Adžaga, Nikola ; Filipin, Alan ; Franušić, Zrinka
clanak
Monatshefte für Mathematik

The extension of the D(−k)-triple {;1, k, k + 1}; to a quadruple

2022., Adedji, Norbert Kouessi ; Filipin, Alan ; Togbe, Alain
clanak
Acta mathematica Hungarica

On D(−1)-triples {;1,4p^2+1,1−p}; in the ring Z[√p] with a prime p

2022., Filipin, Alan ; Jukić Bokun, Mirela ; Soldo, Ivan
clanak
Periodica mathematica Hungarica

The problem of the extension of D(4)-triple {;1,b,c};

2022., Adedji, Kouessi Norbert ; Filipin, Alan ; Togbe, Alain
clanak
Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti

On the family of Diophantine pairs {;P_{;;2k};,P_{;2k+2};};

2022., Adedji, Kouessi Norbert ; Filipin, Alan ; Togbe, Alain
clanak
The Fibonacci quarterly

The Extension of the D(-k)-pair {;k,k+1}; to a Quadruple

2022., Adžaga, Nikola ; Filipin, Alan ; Fujita, Yasutsugu
clanak
Periodica mathematica Hungarica

Padovan and Perrin numbers which are products of two repdigits in base b

2021., Adedji, Kouessi Norbert ; Filipin, Alan ; Togbe, Alain
clanak
Results in mathematics

The Extensibility of the Diophantine Triple {;2,b,c};

2021., Adžaga, Nikola ; Filipin, Alan ; Jurasić, Ana
clanak
Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica

Diophantine quadruples in Z[i][X]

2021., Filipin, Alan ; Jurasić, Ana
clanak
Periodica mathematica Hungarica

Recent Results on Diophantine Sets

2021., Filipin, Alan
nista
International Day of Science

An Infinite Two-Parameter Family of Diophantine Triples

2020., Cipu, Mihai ; Filipin, Alan ; Fujita, Yasutsugu
clanak
Bulletin of the Malaysian Mathematical Sciences Society

Diophantine pairs that induce certain Diophantine triples

2020., Cipu, Mihai ; Filipin, Alan ; Fujita, Yasutsugu
clanak
Journal of number theory

Nonexistence of D(4)-quintuples

2019., Bliznac Trebješanin, Marija ; Filipin, Alan
clanak
Journal of number theory

A polynomial variant of a problem of Diophantus and its consequences

2019., Filipin, Alan ; Jurasić, Ana
clanak
Glasnik matematički

The extension of some Diophantine triples

2019., Filipin, Alan ; Cipu, Mihai ; Fujita, Yasutsugu
sazetak
The 2nd Mediterranean International Conference of Pure&Applied Mathematics and Related Areas

On the extension of D(-k)-pair {;k, k+1};

2019., Filipin, Alan ; Adžaga, Nikola ; Fujita Yasutsugu
sazetak
24th Central European Number Theory Conference

Diophantine quadruples in Z[i][X]

2019., Filipin, Alan ; Jurasić, Ana
sazetak
31st Journées Arithmétiques

A polynomial variant of the problem of Diophantus

2019., Filipin, Alan ; Jurasić, Ana
sazetak
Diophantine Analysis and Related Fields 2019

On the Polynomial Quadruples with the Property D(-1;1)

2018., Bliznac Trebješanin, Marija ; Filipin, Alan ; Jurasić, Ana
clanak
Tokyo Journal of Mathematics

The extension of the infinite two-parameter family of Diophantine triples

2018., Filipin, Alan ; Cipu, Mihai ; Fujita, Yasutsugu
nista
Conference on Diophantine m-tuples and Related Problems II

On the extensibility of the D(4)-triple {; ; k-2, k+2, 4k}; ; over Gaussian integers

2017., Bayad, Abdelmejid ; Dossavi-Yovo, Appolinaire ; Filipin, Alan ; Togbe, Alain
clanak
Notes on number theory and discrete mathematics

Recent results on Diophantine sets

2017., Filipin, Alan
sazetak
Diophantine Analysis and Related Fields 2017

On the extension of D(-8k^2)-pair (8k^2, 8k^2+1)

2017., Adžaga, Nikola ; Filipin, Alan
clanak
Moscow Mathematical Journal

Nonexistence of D(4)-quintuples

2017., Bliznac Trebješanin, Marija ; Filipin, Alan
sazetak
30th Journées Arithmétiques

The extension of some D(4)-pairs

2017., Filipin, Alan
clanak
Notes on number theory and discrete mathematics

Nonexistence of D(4)-quintuples

2017., Filipin, Alan ; Bliznac Trebješanin, Marija
sazetak
19TH ÖMG CONGRESS AND ANNUAL DMV MEETING

A polynomial variant of a problem of Diophantus and its consequences

2017., Jurasić, Ana ; Filipin, Alan
sazetak
19th OMG Congress and Annual DMV Meeting

Bounds for Diophantine quintuples II

2016., Cipu, Mihai ; Filipin, Alan ; Fujita, Yasutsugu
clanak
Publicationes mathematicae

Extension of a parametric family of Diophantine triples in Gaussian integers

2016., Bayad, Abdelmejid ; Filipin, Alan ; Togbe, Alain
clanak
Acta mathematica Hungarica

On the size of Diophantine m-tuples for linear polynomials

2016., Filipin, Alan ; Jurasić, Ana
clanak
Miskolc Mathematical Notes

An upper bound for the number of Diophantine quintuples

2016., Bliznac, Marija ; Filipin, Alan
clanak
Bulletin of the Australian Mathematical Society

The extendibility of D(4)-pairs {;F_{;2k};, F_{;2k+6};}; and {;P_{;2k};, P_{;2k+4};};

2016., Baćić Đuračković, Ljubica ; Filipin, Alan
clanak
Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti

On the extendibility of Diophantine pairs

2016., Filipin, Alan ; Fujita, Yasutsugu ; Togbe, Alain
sazetak
6th Croatian Mathematical Congress

Upper bound on number of D(4)-quintuples

2016., Bliznac, Marija ; Filipin, Alan
nista
6th Croatian Mathematical Congress

D(4)-pairs {; ; F_{; ; 2k}; ; , F_{; ; 2k+6}; ; }; ; and {; ; P_{; ; 2k}; ; , P_{; ; 2k+4}; ; }; ;

2016., Baćić, Ljubica ; Filipin, Alan
sazetak
6th Croatian Mathematical Congress

Linear Forms in Logarithms

2016., Bujačić, Sanda ; Filipin, Alan

On the existence of Diophantine quintuples

2016., Filipin, Alan ; Cipu, Mihai ; Fujita, Yasutsugu
sazetak
14th Meeting of the Canadian Number Theory Association

On the strong version of Diophantine quintuple conjecture

2016., Filipin, Alan ; Fujita, Yasutsugu ; Togbe, Alain
sazetak
Conference on Elementary and analytic number theory (ELAZ 2016)

The extendibility of D(4)-pair {;F_{;2k};, 5F_{;2k};};

2015., Filipin, Alan
clanak
The Fibonacci quarterly

Some recent results on polynomial Diophantine m-tuples

2015., Filipin, Alan ; Jurasić, Ana
sazetak
29th Journees Arithmetiques

On the size of Diophantine m-tuples for linear polynomials

2015., Jurasić, Ana ; Filipin, Alan
sazetak
29th Journees Arithmetiques

On the number of D(4)-quintuples

2015., Baćić, Ljubica ; Filipin, Alan
sazetak
29th Journées Arithmétiques

On Diophantine quintuples and D(-1)-quadruples

2014., Elsholtz, Christian ; Filipin, Alan ; Fujita, Yasutsugu
clanak
Monatshefte für Mathematik

The extendibility of Diophantine pairs I : the general case

2014., Filipin, Alan ; Fujita, Yasutsugu ; Togbe, Alain
clanak
Glasnik matematički

A note on the number of D(4)-quintuples

2014., Baćić, Ljubica ; Filipin, Alan
clanak
Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti

The extendibility of Diophantine pairs II : Examples

2014., Filipin, Alan ; Fujita, Yasutsugu ; Togbe, Alain
clanak
Journal of number theory

The extension of D(4)-pair {;k-2, k+2};

2014., Filipin, Alan
sazetak
Conference on Diophantine m-tuples and related problems

On the existence of Diophantine quintuples

2014., Filipin, Alan
sazetak
Workshop on Number Theory and Algebra on the occasion of 60th birthday of Ivica Gusić

D(4)-pair {;a, b}; and its extension

2014., Baćić, Ljubica ; Filipin, Alan
sazetak
Workshop on Number Theory and Algebra on the occasion of 60th birthday of Ivica Gusić

The number of Diophantine quintuples II

2013., Filipin, Alan ; Fujita, Yasutsugu
clanak
PUBLICATIONES MATHEMATICAE-DEBRECEN

On the family of D(4)-triples {; ; k − 2, k + 2, 4k^3 − 4k}; ;

2013., Baćić, Ljubica ; Filipin, Alan
clanak
Bulletin of the Belgian Mathematical Society Simon Stevin

D(4)-pair {;k-2, k+2}; and its extension

2013., Filipin, Alan ; Baćić, Ljubica
sazetak
Erdös Centennial

The extendibility of D(4)-pairs

2013., Baćić, Ljubica ; Filipin, Alan
clanak
Mathematical communications

On the extensibility of D(4)-pair {; ; k−2, k+2}; ;

2013., Baćić, Ljubica ; Filipin, Alan
clanak
Journal of combinatorics and number theory

The non-extendibility of some parametric families of D(-1)-triples

2012., Filipin, Alan ; Fujita, Yasutsugu ; Mignotte, Maurice
clanak
Quarterly journal of mathematics

The relative upper bound for the third element in a D(−1)-quadruple

2012., Filipin, Alan ; Fujita, Yasutsugu
clanak
Mathematical Communications

On a family of two-parametric D(4)-triples

2012., Filipin, Alan ; He, Bo ; Togbe, Alain
clanak
Glasnik Matematicki

There are only finitely many D(4)-quintuples

2011., Filipin, Alan
clanak
The Rocky Mountain journal of mathematics

The extension of D(-k^2)-triple {;1, k^2 + 1, k^2 + 4}; with k prime

2011., Filipin, Alan ; Fujita, Yasutsugu
sazetak
27th Journees Arithmetiques

The D(−k^2)-triple {;1, k^2 +1, k^2 +4}; with k prime

2011., Filipin, Alan ; Fujita, Yasutsugu
clanak
Glasnik matematički

On the polynomial parametric family of the sets with the property D(-1 ; 1)

2010., Filipin, Alan
clanak
Boletin de la Sociedad Matematica Mexicana

On the D(4)-triple {;F_{;2k};, F_{;2k+6};, 4F_{;2k+4};};

2010., Filipin, Alan ; He, Bo ; Togbe, Alain
clanak
The Fibonacci quarterly

The number of D(−1)-quadruples

2010., Filipin, Alan ; Fujita, Yasutsugu
clanak
Mathematical communications

On the number of D(-1)-quadruples

2010., Filipin, Alan ; Fujita, Yasutsugu
sazetak
Number Theory and Its Applications. An international conference dedicated to Kalman Gyory, Attila Petho, Janos Pintz and Andras Sarkozy

On the size of sets in which xy + 4 is always a square

2009., Filipin, Alan
clanak
Rocky Mountain Journal of Mathematics

An irregular D(4)-quadruple cannot be extended to a quintuple

2009., Filipin, Alan
clanak
Acta Arithmetica

Sets in which xy+4 is always a square

2009., Filipin, Alan
nista
Winter School on Explicit Methods in Number Theory

On the family of Diophantine triples {;k+2, 4k, 9k+6};

2009., Filipin, Alan ; Togbe, Alain
clanak
Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis

There are only finitely many D(4)-quintuples

2009., Filipin, Alan
sazetak
26th Journées Arithmétiques

On the uniqueness of extension of twoparametric family of D(4)-triples

2009., Filipin, Alan ; He, Bo ; Togbe, Alain
sazetak
17th ÖMG Congress — Annual DMV Meeting

There does not exist a D(4)-sextuple

2008., Filipin, Alan
clanak
Journal of Number Theory

The additive unit structure of pure quartic complex fields

2008., Filipin, Alan ; Tichy, Robert ; Ziegler, Volker
clanak
Functiones et Approximatio Commentarii Mathematici

Any polynomial D(4)-quadruple is regular

2008., Filipin, Alan ; Fujita, Yasutsugu
clanak
Mathematical Communications

The unit sum number problem in some number fields

2008., Filipin, Alan ; Tichy Robert ; Ziegler, Volker
sazetak
4th Croatian Mathematical Congress

On the quantitative unit sum number problem - an application of the Subspace Theorem

2008., Filipin, Alan ; Tichy, Robert ; Ziegler, Volker
clanak
Acta Arithmetica

Any D(4)-quintuple contains a regular quadruple

2008., Filipin, Alan
sazetak
Canadian Number Theory Association X Meeting (CNTA X)

Extensions of some parametric families of D(16)-triples

2007., Filipin, Alan
clanak
International Journal of Mathematics and Mathematical Sciences

Effective solution of the D(-1)-quadruple conjecture

2007., Dujella, Andrej ; Filipin, Alan ; Fuchs, Clemens
clanak
Acta Arithmetica

There does not exist a D(4)-sextuple

2007., Filipin, Alan
sazetak
25th Journees Arithmetiques

The unit sum number problem for number fields

2007., Ziegler, Volker ; Tichy, Robert ; Filipin, Alan
sazetak
25th Journees Arithmetiques

The unit sum number problem of some number fields

2007., Filipin, Alan
nista
Zahlentheoretisches Kolloquium

Sustavi pellovskih jednadžbi i problem proširenja nekih Diofantovih trojki

2006., Filipin, Alan
doktorska disertacija

On the D(-1)-quadruple conjecture

2006., Filipin, Alan ; Dujella, Andrej ; Fuchs, Clemens
sazetak
Canadian Number Theory Association IX Meeting

Non-extendibility of D(-1)-triples of the form {; ; 1, 10, c}; ;

2005., Filipin, Alan
clanak
International Journal of Mathematics and Mathematical Sciences

Nastavne djelatnosti

Nastavni rad (na Građevinskom fakultetu):

  • 2003. honorarno izvodim vježbe za Matematiku II i Matematiku III
  • 2004.-2007. izvodim vježbe za Matematiku I, Matematiku II, Matematiku III i OII 2
  • 2008.-          izvodim predavanja za Matematiku I, Matematiku II, Vjeorjatnost i statistiku i Primijenjenu statistiku

Nastavni rad (na drugim fakultetima):

  • u akademskoj godini 2009./2010. izvodim predavanja iz kolegija "Linearne forme u logaritmima i diofanstka analiza" na doktorskom studiju matematike, na PMF-matematičkom odjelu (skripta)
  • u akademskoj godini 2014./2015. izvodim predavanja iz kolegija "Pellove jednadžbe" na doktorskom studiju matematike na PMF-matematičkom odsjeku (bilješke s predavanja, prva zadaća, druga zadaća, treća zadaća, četvrta zadaća)
  • u akadeskoj godini 2019./2020. izvodim predavanja iz kolegija "Diofantovi skupvi" na doktorskom studiju matematike na PMF-matematičkom odsjeku (web stranica kolegija)

Mentorstva (završena):

  • Senka Ibrahimpašić, magistarski rad "Diofantske m-torke" (Bihać, 18.4.2014.)
  • Ljubica Baćić, doktorska disertacija "Skupovi u kojima je xy + 4 potpun kvadrat i problem proširenja nekih parametarskih Diofantskih trojki" (Zagreb, 10.7.2014.)
  • Jasna Bagović, diplomski rad "Metode rješavanja Pellove jednadžbe" (PMF-MO, Zagreb, 26.9.2015.)
  • Marija Bliznac Trebješanin, doktorska disertacija "Diofantske D(4)-m-torke i srodni problemi" (Zagreb, 25.1.2018.)
  • Nikola Adžaga, doktorska disertacija "Diofantove m-torke u prstenima cijelih brojeva" (Zagreb, 18.5.2018.)
  • Marina Ilić, diplomski rad "Primjena linearnih formi u logaritmima na rješavanje diofantskih jednadžbi" (PMF-MO, Zagreb, 28.11.2018.)
  • Kouessi Norbert Adedji, magistarski rad "Conjectures on Diophantine sets" (IMSP, Dangbo, Benin, 13.9.2019.)
  • Kouessi Norbert Adedji, doktorska disertacij "Study of some Diophantine sets and other Diophantine equations" (IMSP, Dangbo, Benin, 10.8.2022.)

Izabrane publikacije

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1. A. Filipin, Non-extendibility of D(-1)-triples of the form {1,10,c}, Internat. J. Math. Math. Sci. 35 (2005) 2217-2226.

2. A. Dujella, A. Filipin, C. Fuchs, Effective solution of the D(-1)-quadruple conjecture, Acta Arith. 128 (2007), 319-338.

3. A. Filipin, Extensions of some parametric families of D(16)-triples, Internat. J. Math. Math. Sci. 2007 (2007), Article ID 63739, 12 pages.

4. A. Filipin, There does not exist a D(4)-sextuple, J. Number Theory 128 (2008), 1555-1565.

5. A. Filipin, Y. Fujita, Any polynomial D(4)-quadruple is regular, Math. Commun. 13 (2008), 45-55.

6. A. Filipin, R. Tichy, V. Ziegler, On the quantitative unit sum number problem - an application of the Subspace Theorem, Acta Arith. 133 (2008), 297-308.

7. A. Filipin, R. Tichy, V. Ziegler, The additive unit structure of pure quartic complex fields, Functiones et Approximatio, Commentarii Mathematici 39 (2008), 113-131.

8. A. Filipin, On the size of sets in which xy + 4 is always a square, Rocky Mountain J. Math. 39 (2009), 1195-1224.

9. A. Filipin, An irregular D(4)-quadruple cannot be extended to a quintuple, Acta Arith. 136 (2009), 167-176.

10. A. Filipin, A. Togbe, On the family of Diophantine triples {k+2, 4k, 9k+6}, Acta Math. Acad. Paedagog. Nyhazi. 25 (2009), 145-153.

11. A. Filipin, On the polynomial parametric family of the sets with the property D(-1;1), Bol. Soc. Mat. Mexicana 16 (2010), 1-8.

12. A. Filipin, B. He, A. Togbe, On the D(4)-triple { F_{2k}, F_{2k+6}, 4F_{2k+4} }, Fibonacci Quart. 48 (2010), 219-227.

13. A. Filipin, Y. Fujita, The number of D(-1)-quadruples, Math. Commun. 15 (2010), 387-391.

14. A. Filipin, Y. Fujita, The D(-k^2)-triple {1,k^2+1,k^2+4} with k prime, Glas. Mat. Ser. III 46 (2011), 311-323.

15. A. Filipin, There are only finitely many D(4)-quintuples, Rocky Mountain J. Math. 41 (2011), 1847-1860.

16. A. Filipin, Y. Fujita, The relative upper bound for the third element in a D(-1)-quadruple, Math. Commun. 17 (2012), 13-19.

17. A. Filipin, B. He, A. Togbe, On a family of two-parametric D(4)-triples, Glas. Mat. Ser. III, 47 (2012), 31-51.

18. A. Filipin, Y. Fujita, M. Mignotte, The non-extendibility of some parametric families of D(-1)-triples, Q. J. Math. 63 (2012), 3; 605-621.

19. A. Filipin, Y. Fujita, The number of Diophantine quintuples II, Publ. Math. Debrecen 82/2 (2013), 293-308.

20. Lj. Baćić, A. Filipin, On the family of D(4)-triples {k-2,k+2,4k^3-4k}, Bull. Belg. Math. Soc. Simon Stevin, 20 (2013), 777-787.

21. Lj. Baćić, A. Filipin, On the extensibility of D(4)-pair {k-2,k+2}, J. Comb. Number Theory, 5 (2013), 181-197.

22. Lj, Baćić. A. Filipin, On the extendibility of D(4)-pairs, Math. Communn., 18 (2013), 447-456.

23. A. Filipin, Y. Fujita, A. Togbe, The extendibility of Diophantine pairs I: the general case, Glas. Mat. Ser. III, 49 (2014), 25-36.

24. A. Filipin, Y. Fujita, A. Togbe, The extendibility of Diophantine pairs II: examples, Journal of Number Theory, 145 (2014), 604-631.

25. C. Elsholtz, A. Filipin, Y. Fujita, On Diophantine quintuples and D(-1)-quadruples, Monatsh. Math., 175 (2) (2014), 227-239.

26. Lj. Baćić, A.Filipin, A note on the number of D(4)-quintuples, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., 18 (2014), 7-13.

27. A. Filipin, The extendibility of D(4)-pair {F_{2k},5F_{2k}}, Fibonacci Quart., 53 (2015), 124-129.

28. M. Cipu, A. Filipin, Y. Fujita, Bounds for Diophantine quintuples II, Publ. Math. Debrecen, 86 (2016), 59-78.

29. A. Bayad, A. Filipin, A. Togbe, Extension of a parametric family of Diophantine triples in Gaussian integers, Acta Math. Hung., 148 (2016), 312-327.

30. M. Bliznac, A. Filipin, An upper bound for the number of Diophantine quintuples, Bull. Aust. Math. Soc., 94 (2016) , 384-394.

31. Lj. Baćić Đuračković, A. Filipin, The extendibility of D(4)-pairs {F_{2k}, F_{2k+6}} and {P_{2k}, P_{2k+4}},  Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., 20 (2016) , 27-35.

32. A. Filipin, A. Jurasić, On the size of Diophantine m-tuples for linear polynomials, Miskolc Math. Notes, 17 (2016), 861-876. 

33. A. Filipin, The extension of some D(4)-pairs, Notes Number Theory Discrete Math., 23 (2017), 126-135.

34. A. Bayad, A. Dossavi-Yovo, A. Filipin, A. Togbe, On the extensibility of D(4)-triple {k-2, k+2, 4k} over Gaussian integers, Notes Number Theory Discrete Math., 23 (2017), 1-26.

35. N. Adžaga, A. Filipin, On the extension of D(-8k^2)-pair {8k^2, 8k^2 + 1}, Mosc. Math. J., 17 (2017), 165-174.

36. M. Bliznac Trebješanin, A. Filipin, A. Jurasić, On the polynomial quadruples with the property D(-1;1), Tokyo J. Math., 41 (2018), 527-540.

37. M. Bliznac Trebješanin, A. Filipin, Nonexistence of D(4)-quintuples, Journal of Number Theory, 194 (2019), 170-217.

38. A. Filipin, A. Jurasić, A polynomial variant of a problem of Diophantus and its consequences, Glas. Mat. Ser. III, 54 (2019), 21-52.

39. M. Cipu, A. Filipin, Y. Fujita, An infinite two-parameter family of Diophantine triples, Bulletin of the Malaysian Mathematical Sciences Society, 43 (2020), 481-498.

40. M. Cipu, A. Filipin, Y. Fujita, Diophantine pairs that induce certain Diophantine triples, Journal of Number Theory, 210 (2020), 433-475.

41. A. Filipin, A. Jurasić, Diophantine quadruples in Z[i][X], Period. Math. Hungar., 82 (2021), 198-212.

42. N. Adžaga, A. Filipin, A. Jurasić, The extensibility of the Diophantine triple {2, b, c}, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat., 29(2) (2021), 5-24.

43. K. N. Adedji, A. Filipin, A. Togbé, Padovan and Perrin numbers which are products of two repdigits in base b, Results in Mathematics, 76 (2021), article number 193, 24 pages.

44. N. Adžaga, A. Filipin, Y. Fujita, The extension of the  D(-k)-pair {k, k+ 1} to a quadruple, Period. Math. Hungar. 166(2) (2021), 407-422.

45. A. Filipin, M. Jukic Bokun, I. Soldo, On D(-1)-triples {1, 4p^2 + 1, 1 - p} in the ring Z[√-p] with a prime p, Period. Math. Hungar. 85(2) (2022), 292-302.

46. K. N. Adedji, A. Filipin, A. Togbé, The problem of the extension of D(4)-triple {1, b, c}, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., 26 (2022), 21-43.

47. K. N. Adedji, A. Filipin, A. Togbé, On the family of Diophantine pairs {P_{2k}, P_{2k+2}}, Fibonacci Quart, 60(1) (2022), 25-39.

48. A. Filipin, A. Jurasić, On the existence of D(-3)-quadruples in Z[X], Glas. Mat. Ser. III 57(77) (2022), 203-219.

49. N. Adžaga, A. Filipin, Z. Franušić, On the extensions of the Diophantine triples in Gaussian integers, Monats. Math. 197(4) (2022), 535-563.

50.  K. N. Adedji, A. Filipin, A. Togbé, The extension of the D(-k)-triple {1, k, k+1} to a quadruple, Acta Math. Hung., 166(2) (2022), 407-422.

51. K. N. Adedji, A. Filipin, S. E. Rihane, A. Togbé, Fibonacci or Lucas numbers which are concatenations of two g-repdigits, Fibonacci Quart., to appear.

52. A. Filipin, L. Szalay, Triangular Diophantine tuples from {1, 2}, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., to appear.

53. K. N. Adedji, A. Filipin, S. E. Rihane, A. Togbé, Pell or Pell-Lucas numbers as concatenations of two repdigits in base b, preprint.

54. K. N. Adedji, M. Blznac Trebješanin, A. Filipin, A. Togbe, On the D(4) pairs {a, ka} with k ∈ {2, 3, 6}, preprint.

55. K. N. Adedji, A. Filipin, A. Togbé, Fibonacci and Lucas numbers as products of three repdigits in base g, preprint.

PRIOPĆENJA NA KONFERENCIJAMA

1. A. Filipin, A. Dujella, C. Fuchs, On the D(-1)-quadruple conjecture, CNTA IX Meeting, Vancouver, Kanada, 9.-14.7.2006.

2. A. Filipin, There does not exist a D(4)-sextuple, 25th Journées Arithmétiques, Edinburgh, Velika Britanija, 2.-6.7.2007.

3. A. Filipin, R. Tichy, V. Ziegler, The unit sum number problem in some number fields, 4th Croatian Mathematical Congress, Osijek, 17.-20.6.2008.

4. A. Filipin, Any D(4)-quintuple contains a regular quadruple, CNTA X Meeting, Waterloo, Kanada, 13.-18.7.2008.

5. A. Filipin, Sets in which xy+4 is always a square, Winter School on Explicit Methods in Number Theory, Debrecen, Mađarska, 26.-30.1.2009.

6. A. Filipin, There are only finitely many D(4)-quintuples, 26th Journées Arithmétiques, Saint-Etienne, Francuska, 6.-10.7.2009.

7. A. Filipin, B. He, A. Togbe, On the uniqueness of extension of twoparametric family of D(4)-triples,ÖMG+DMV Conference, Graz, Austrija, 20.-25.9.2009.

8. A. Filipin, Y. Fujita, On the number of D(-1)-quadruples, Number Theory and Its Applications, Debrecen, Mađarska, 4.-8.10.2010.

9. A. Filipin, Y. Fujita, The extension of D(-k^2)-triple {1,k^2+1,k^2+4} with k prime, 27th Journées Arithmétiques, Vilnius, Litva, 27.6.-1.7.2011.

10. A. Filipin, Lj. Baćić, D(4)-pair {k-2,k+2} and its extension, Erdős Centennial, Budimpešta, Mađarska, 1.-5.7.2013. (poster)

11. A. Filipin, The extension of D(4)-pair {k-2,k+2} (and some related problems), Conference on Diophantine m-tuples and related problems, Westville, S.A.D., 13.-15.11.2014. (plenarno izlaganje)

12. A. Filipin, On the existence of Diophantine quintuples, Workshop on Number Theory and Algebra on the occasion of 60th birthday of Ivica Gusić, Zagreb, Hrvatska, 26.-28.11.2014. (pozvano predavanje)

13. A. Filipin, A. Jurasić, Some recent results on polynomial Diophantine m-tuples, 29th Journées Arithmétiques, Debrecen, Mađarska, 6.-10.7.2015.

14. A. Filipin, Y. Fujita, A. Togbe, On the extendibility of Diophantine pairs, 6th Croatian Mathematical Congress, Zagreb, Hrvatska, 14.-17.6.2016.

15. A. Filipin, M. Cipu, Y. Fujita, On the existence of Diophantine quintuples, CNTA XIV Meeting, Calgary, Kanada, 20.-24.7.2016.

16. A. Filipin, Y. Fujita, A. Togbe, On the strong version of Diophantine quintuple conjecture, ELAZ 2016, Strobl, Austrija, 5.-9.9.2016. (poster + kratko priopćenje)

17. A. Filipin, Recent results on Diophantine sets, Diophantine Analysis and Related Fields 2017, Tokyo, Japan, 7.-9.1.2017. (pozvano predavanje)

18. A. Filipin, M. Bliznac Trebješanin, Nonexistence of D(4)-quintuples, 19th ÖMG Congress and Annual DMV Meeting, Salzburg, Austrija, 11.-15.9.2017.

19. A. Filipin, M. Cipu, Y. Fujita, The extension of infinite two-parameter family of Diophantine triples, Conference on Diophantine m-tuples and related problems II, Westville/Hammond, S.A.D., 15.-17.10.2018. (plenarno izlaganje)

20. A. Filipin, A. Jurasić, A polynomail variant of the problem of Diophantus, Diophantine Analysis and Related Fields 2019, Tsukuba, Japan, 7.-9.3.2019. (pozvano predavanje)

21. A. Filipin, A. Jurasić. Diophantine quadruples in Z[i][X], 31st Journées Arithmétiques, Istanbul, Turska, 1.-5.7.2019.

22. A. Filipin, M. cipu, Y. Fujita, The extension of some Diophantine triples, The 2nd Mediterranean International Conference of Pure & Applied Mathematics and Related Areas 2019, Pariz, Francuska, 28.-31.8.2019. (pozvano predavanje)

23. A. Filipin, N. Adžaga, Y. Fujita, On the extension of D(-k)-pair {k, k+1}, 24th Central European Number Theory Conference, Komarno, Slovačka, 2.-6.9.2019.

24. A. Filipin, Recent result on Diophantine sets, International day of science, Sopron, Mađarska, 23.3.2021. (pozvano predavanje, online)

25. A. Filipin, A. Jurasić, Polynomial D(-3)-quadruples, Number Theory Conference 2022 In honour of
Professors Kálmán Győry, János Pintz and András Sárközy, Debrecen, Mađarska, 4.7.2022.

26. A. Filipin, K. N. Adedji, A. Togbe, Products of two repdigits in some recurrence sequences, The Twentieth International Conference on Fibonacci Numbers and Their Applications, Sarajevo, Bosna i Hercegovina, 25.7.2022.

POZVANA PREDAVANJA (na seminarima, znanstvenim kolokvijima, manjim znanstvenim skupovima)

1. A. Filipin, There are only finitely many D(-1)-quadruples, TU Graz, Austrija, 28.9.2006.

2. A. Filipin, The unit sum number problem of some number fields, TU Graz, Austrija, 14.12.2007.

3. A. Filipin, On D(4)-m-tuples, TU Graz, Austrija, 7.11.2008.

4. A. Filipin, The non-extensibility of D(-1)-triple {1,k^2+1,c} with k prime, TU Graz, Austrija, 3.12.2010.

5. A. Filipin, On the extension of D(-1)-triples, TU Graz, Austrija, 10.11.2011.

6. A. Filipin, On Diophantine m-tuples, Tokyo University of Science, Japan, 26.6.2014.

7. A. Filipin, Some results on polynomial Diophantine m-tuples, TU Graz, Austrija, 13.3.2015.

8. A. Filipin, On Diophantine quintuple conjecture, Purdue University North Central, Westville, S. A. D., 21.9.2015.

9. A. Filipin, Dirichletov princip, Pedagoški fakultet Univerziteta u Bihaću, Bosna i Hercegovina, 17.10.2015.

10. A. Filipin, Polynomial version of Diophantine m-tuples, University of Bucharest, Rumunjska, 16.3.2016.

11. A. Filipin, Najnoviji rezultati o Diofantovim petorkama, Sveučilište J. J. Strossmayera, Odjel za matematiku, Osijek, 14.4.2016.

12. A. Filipin, Survey on Diophantine m-tuples, TU Graz, Austrija, 9.5.2016.

13. A. Filipin, The proof of the non-existance of D(4)-quintuples, South China Normal University, Guangzhou, Kina, 8.1.2018.

14. A. Filipin, The uniqueness of the extension of infinite two-parameter family of Diophantine triples, TU Graz, Austrija, 21.9.2018.

15. A. Filipin, On the extendibility of D(-k)-triples of the form {k, k+1, c}, Institut de Mathématiques et de Sciences Physiques, Dangbo, Benin, 23.5.2019.

16. A. Filipin, The extension of D(-k)-pair {k, k+1}, Diophantine Number Theory Research Seminar, University of Salzburg, Austrija, 30.4.2021. (online)

17. A. Filipin, On the problem of Padovan and Perrin numbers which are products of two repdigits, University of Salzburg, Austrija, 5.5.2022.

18. A. Filipin, Triangular Diophantine sets, Purdue University Northwest, Westville, S. A. D., 13.10.2022.

19. A. Filipin, On the Triangular Diophantine m-tuples, TU Graz, Austrija, 15.12.2022.

Profesionalni interesi i članstva

Područja istraživanja:

  • Teorija brojeva
  • Diofantske jednadžbe, sustavi simultanih pellovskih jednadžbi
  • Diofantove m-torke

Članstva:

  • član Seminara za teoriju brojeva i algebru, čiji su voditelji prof.dr.sc. Andrej Dujella, prof.dr.sc. Ivica Gusić, prof.dr.sc. Alan Filipin, prof.dr.sc. Borka Jadrijević i prof.dr.sc. Filip Najman 
  • član Hrvatskog matematičkog društva

Članstva u tijelima/odborima Građevinskog fakulteta:

  • 2008.-2019. predsjednik Vijeća 1. godišta
  • 2010.-2020. predsjednik Stegovnog suda za studente
  • 2012.-2018. član Povjerenstva za međunarodnu suradnju
  • 2012.-2020. predstojnik Zavoda za matematiku
  • 2012.-2018. član Odbora za jamstvo kvalitete
  • 2012.-2021. predstavnik Građeviskog fakulteta u vijeću PMF-MO
  • 2017.-2018. član Odbora za znanost
  • 2018.-2020., 2022.- član Odbora za nastavu
  • 2022.-          pročelnik Katedre za matematičke predmete

Izabrani projekti

  • 2006.-2007. suradnik na zajedničkom hrvatsko-austrijskom projektu "Algoritmic solutions of Diophantine equations and applications to cryptography II"
  • 2007.- 2014. suradnik na projektu Diofantske jednadžbe i eliptičke krivulje , koje je financiralo Ministarstvo znanosti, obrazovaja i športa
  • 2008.-2009. suradnik na zajedničkom hrvatsko-austrijskom projektu "Diophantine equations and additive representations"
  • 2009.-2011. suradnik na zajedničkom hrvatsko-mađarskom projektu "Number theory and Cryptography"
  • 2010.-2011. suradnik na zajedničkom hrvatsko-austrijskom projektu "Arithmetic-combinatorial problems and applications"
  • 2013.-2014. suradnik na zajedničkom hrvatsko-francuskom, projektu "Polynomial root separation"
  • 2014.-2018. suradnik na projektu "Diophantine m-tuples, elliptic curves, Thue and index form equations" financiranom od Hrvatske zaklade za znanost
  • 2016.-2017. voditelj (s hrvatske strane) na zajedničkom hrvatsko-austrijskom projektu "Classical Problems of Diophant, Fermat and Ritt using New Analytic and Algebraic Techniques"
  • 2018.-2022. suradnik na projektu "Diofantska geometrija i primjene" financiranom od Hrvatske zaklade za znanost
  • 2020.-2021. suradnik na zajedničkom hrvatsko-austrijskom projektu "Suvremeni pristup nekim klasičnim diofantskim problemima"
  • 2021.-2023. voditelj (s hrvatske strane) na zajedničkom hrvatsko-mađarskom projektu "Application of linear recurrences in number theory and combinatorics"

Povijest zaposlenja

  • 2004.-         University of Zagreb, Faculty of Civil Engineering, Department of Mathematics
  • 2004.-2006. asistent
  • 2006.-2008. viši asistent
  • 2008.-2012. docent
  • 2012.-2017. izvanredni profesor
  • 2017.-          redoviti profesor