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Fibonacci and Lucas numbers as products of three repdigits in base g
On the D(4)-pairs {;a,ka}; with k ∈ {;2,3,6};
Triangular Diophantine tuples from {;1, 2};
Fibonacci or Lucas numbers which are concatenations of two g-repdigits
Polynomial D(-3)-quadruples
Diofantovi skupovi
Products of two repdigits in some recurrence sequences
On the existence of D(-3)-quadruples in Z[X]
On the extensions of the Diophantine triples in Gaussian integers
The extension of the D(−k)-triple {;1, k, k + 1}; to a quadruple
On D(−1)-triples {;1,4p^2+1,1−p}; in the ring Z[√p] with a prime p
The problem of the extension of D(4)-triple {;1,b,c};
On the family of Diophantine pairs {;P_{;;2k};,P_{;2k+2};};
The Extension of the D(-k)-pair {;k,k+1}; to a Quadruple
Padovan and Perrin numbers which are products of two repdigits in base b
The Extensibility of the Diophantine Triple {;2,b,c};
Diophantine quadruples in Z[i][X]
Recent Results on Diophantine Sets
An Infinite Two-Parameter Family of Diophantine Triples
Diophantine pairs that induce certain Diophantine triples
Nonexistence of D(4)-quintuples
A polynomial variant of a problem of Diophantus and its consequences
The extension of some Diophantine triples
On the extension of D(-k)-pair {;k, k+1};
Diophantine quadruples in Z[i][X]
A polynomial variant of the problem of Diophantus
On the Polynomial Quadruples with the Property D(-1;1)
The extension of the infinite two-parameter family of Diophantine triples
On the extensibility of the D(4)-triple {; ; k-2, k+2, 4k}; ; over Gaussian integers
Recent results on Diophantine sets
On the extension of D(-8k^2)-pair (8k^2, 8k^2+1)
Nonexistence of D(4)-quintuples
The extension of some D(4)-pairs
Nonexistence of D(4)-quintuples
A polynomial variant of a problem of Diophantus and its consequences
Bounds for Diophantine quintuples II
Extension of a parametric family of Diophantine triples in Gaussian integers
On the size of Diophantine m-tuples for linear polynomials
An upper bound for the number of Diophantine quintuples
The extendibility of D(4)-pairs {;F_{;2k};, F_{;2k+6};}; and {;P_{;2k};, P_{;2k+4};};
On the extendibility of Diophantine pairs
Upper bound on number of D(4)-quintuples
D(4)-pairs {; ; F_{; ; 2k}; ; , F_{; ; 2k+6}; ; }; ; and {; ; P_{; ; 2k}; ; , P_{; ; 2k+4}; ; }; ;
Linear Forms in Logarithms
On the existence of Diophantine quintuples
On the strong version of Diophantine quintuple conjecture
The extendibility of D(4)-pair {;F_{;2k};, 5F_{;2k};};
Some recent results on polynomial Diophantine m-tuples
On the size of Diophantine m-tuples for linear polynomials
On the number of D(4)-quintuples
On Diophantine quintuples and D(-1)-quadruples
The extendibility of Diophantine pairs I : the general case
A note on the number of D(4)-quintuples
The extendibility of Diophantine pairs II : Examples
The extension of D(4)-pair {;k-2, k+2};
On the existence of Diophantine quintuples
D(4)-pair {;a, b}; and its extension
The number of Diophantine quintuples II
On the family of D(4)-triples {; ; k − 2, k + 2, 4k^3 − 4k}; ;
D(4)-pair {;k-2, k+2}; and its extension
The extendibility of D(4)-pairs
On the extensibility of D(4)-pair {; ; k−2, k+2}; ;
The non-extendibility of some parametric families of D(-1)-triples
The relative upper bound for the third element in a D(−1)-quadruple
On a family of two-parametric D(4)-triples
There are only finitely many D(4)-quintuples
The extension of D(-k^2)-triple {;1, k^2 + 1, k^2 + 4}; with k prime
The D(−k^2)-triple {;1, k^2 +1, k^2 +4}; with k prime
On the polynomial parametric family of the sets with the property D(-1 ; 1)
On the D(4)-triple {;F_{;2k};, F_{;2k+6};, 4F_{;2k+4};};
The number of D(−1)-quadruples
On the number of D(-1)-quadruples
On the size of sets in which xy + 4 is always a square
An irregular D(4)-quadruple cannot be extended to a quintuple
Sets in which xy+4 is always a square
On the family of Diophantine triples {;k+2, 4k, 9k+6};
There are only finitely many D(4)-quintuples
On the uniqueness of extension of twoparametric family of D(4)-triples
There does not exist a D(4)-sextuple
The additive unit structure of pure quartic complex fields
Any polynomial D(4)-quadruple is regular
The unit sum number problem in some number fields
On the quantitative unit sum number problem - an application of the Subspace Theorem
Any D(4)-quintuple contains a regular quadruple
Extensions of some parametric families of D(16)-triples
Effective solution of the D(-1)-quadruple conjecture
There does not exist a D(4)-sextuple
The unit sum number problem for number fields
The unit sum number problem of some number fields
Sustavi pellovskih jednadžbi i problem proširenja nekih Diofantovih trojki
On the D(-1)-quadruple conjecture
Non-extendibility of D(-1)-triples of the form {; ; 1, 10, c}; ;
Nastavni rad (na Građevinskom fakultetu):
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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.
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