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Diophantine equations
(0037110)

 
 
 
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  Textbooks and scripts
 

1. Červar, Branko; Jadrijević, Borka.
Mathematics 2 / Zulim, Ivan, editor(s).
Split : Fakultet elektrotehnike, strojarstva i brodogradnje, Sveučilište u Splitu, 2006..

2. Gusić, Ivica; Gusić, Jelena; Krajina, Jagoda.
Mathematics 1 (textbook) .
Zagreb : Školska knjiga, 2005.

3. Mrkonjić, Ivan; Gusić, Ivica; Gusić, Jelena.
Mathematics 5, textbook .
Zagreb : Školska knjiga, 2004.

4. Mrkonjić, Ivan; Gusić, Ivica; Gusić, Jelena.
Mathematics 6, textbook .
Zagreb : Školska knjiga, 2004.

5. Mrkonjić, Ivan; Gusić, Ivica; Gusić, Jelena.
Mathematics 7, textbook .
Zagreb : Školska knjiga, 2004.

6. Mrkonjić, Ivan; Gusić, Ivica; Gusić, Jelena.
Mathematics 8, textbook .
Zagreb : Školska knjiga, 2004.

7. Mrkonjić, Ivan; Gusić, Ivica; Gusić, Jelena.
Mathematics 5, handbook for teachers .
Zagreb : Školska knjiga, 2003.

8. Mrkonjić, Ivan; Gusić, Ivica; Gusić, Jelena.
Mathematics 6, handbook for teachers .
Zagreb : Školska knjiga, 2003.

9. Mrkonjić, Ivan; Gusić, Ivica; Gusić, Jelena.
Mathematics 7, handbook for teachers .
Zagreb : Školska knjiga, 2003.

10. Mrkonjić, Ivan; Gusić, Ivica; Gusić, Jelena.
Mathematics 8, handbook for teachers .
Zagreb : Školska knjiga, 2003.
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  Journal articles and review articles in CC journals
 

1. Dujella, Andrej; Fuchs, Clemens; Walsh, Gary P.
Diophantine m-tuples for linear polynomials. II. Equal degrees. // Journal of Number Theory. 120 (2006) , 2; 213-228 (journal article). prilozen text rada

2. Dujella, Andrej; Gusić, Ivica.
Indecomposability of polynomials and related Diophantine equations. // Quarterly journal of mathematics. 57 (2006) , 2; 193-201 (journal article). prilozen text rada

3. Jadrijević, Borka; Ziegler, Volker.
A system of relative Pellian equations and a related family of relative Thue equations. // International Journal of Number Theory. 2 (2006) , 4; 569-590 (journal article). URL link to work

4. Dujella, Andrej; Fuchs, Clemens.
Complete solution of a problem of Diophantus and Euler. // Journal of the London Mathematical Society. 71 (2005) , 1; 33-52 (journal article).

5. Dujella, Andrej; Luca, Florian.
Diophantine m-tuples for primes. // International mathematics research notices. 47 (2005) ; 2913-2940 (journal article). prilozen text rada

6. Dujella, Andrej; Ramasamy, A.M.S.
Fibonacci numbers and sets with the property D(4). // Bulletin of the Belgian Mathematical Society Simon Stevin. 12 (2005) , 3; 401-412 (journal article).

7. Gusić, Ivica.
A characterization of linear polynomials. // Journal of number theory. 115 (2005) , 2; 343-347 (journal article). URL link to workURL link to work

8. Jadrijević, Borka.
A system of Pellian equations and related two-parametric family of quartic Thue equations. // The Rocky Mountain journal of mathematics. 35 (2005) , 2; 547-573 (journal article).

9. Dujella, Andrej.
There are only finitely many Diophantine quintuples. // Journal für die reine und angewandte Mathematik. 566 (2004) , 1; 183-214 (journal article).

10. Dujella, Andrej; Fuchs, Clemens.
Complete solution of the polynomial version of a problem of Diophantus. // Journal of Number Theory. 106 (2004) , 2; 326-344 (journal article).

11. Dujella, Andrej; Jadrijević, Borka.
A family of quartic Thue inequalities. // Acta Arithmetica. 111 (2004) , 4; 61-76 (journal article).

12. Bugeaud, Yann; Dujella, Andrej.
On a problem of Diophantus for higher powers. // Mathematical Proceedings of the Cambridge Philosophical Society. 135 (2003) , 1; 1-10 (journal article).

13. Dujella, Andrej; Fuchs, Clemens.
A polynomial variant of a problem of Diophantus and Euler. // Rocky Mountain Journal of Mathematics. 33 (2003) , 3; 797-811 (journal article).

14. Dujella, Andrej.
On the size of Diophantine m-tuples. // Mathematical Proceedings of the Cambridge Philosophical Society. 132 (2002) ; 23-33 (journal article).

15. Dujella, Andrej; Jadrijević, Borka.
A parametric family of quartic Thue equations. // Acta Arithmetica. 101 (2002) , 2; 159-170 (journal article).
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  Scientific papers in other journals
 

1. Dujella, Andrej; Gusić, Ivica; Tichy, Robert.
On the indecomposabilty of polynomials. // Sitzungsberichte und Anzeiger Mathematisch-naturwissenschaftliche Klasse. Abteilung II : Mathematische, Physikalische und Technische Wissenschaften. 214 (2005) ; 81-88 (journal article). prilozen text radaURL link to work

2. Dujella, Andrej; Petričević, Vinko.
Square roots with many good approximants. // Integers. 5 (2005) , 3; 1-13 (journal article). URL link to work

3. Gusić, Ivica.
A note on generalized derivations of prime rings. // Glasnik matematički. 40 (2005) , 1; 47-49 (journal article).

4. Gusić, Ivica.
A purely algebraic proof of AG inequality. // Mathematical inequalities & applications. 8 (2005) , 2; 191-198 (journal article).

5. Jadrijević, Borka.
On two-parametric family of quartic Thue equations. // Journal de théorie des nombres de Bordeaux. 17 (2005) , 1; 161-167 (journal article).

6. Dujella, Andrej.
Bounds for the size of sets with the property D(n). // Glasnik matematički. 39 (2004) , 2; 199-205 (journal article).

7. Dujella, Andrej.
Continued fractions and RSA with small secret exponent. // Tatra mountains mathematical publications. 29 (2004) ; 101-112 (journal article).

8. Dujella, Andrej.
Diophantine quadruples and Fibonacci numbers. // Bulletin of Kerala Mathematics Association. 1 (2004) , 2; 133-147 (journal article).

9. Dujella, Andrej.
An example of elliptic curve over Q with rank equal to 15. // Proceedings of the Japan Academy. Series A. Mathematical Sciences. 78 (2002) , 7; 109-111 (journal article).

10. Dujella, Andrej.
An extension of an old problem of Diophantus and Euler. II. // The Fibonacci Quarterly. 40 (2002) , 2; 118-123 (journal article).

11. Dujella, Andrej; Deshpande, M. N.
An interesting property of a recurrence related to the Fibonacci sequence. // The Fibonacci Quarterly. 40 (2002) , 2; 157-160 (journal article).

12. Dujella, Andrej; Fuchs, Clemens; Tichy, Robert.
Diophantine m-tuples for linear polynomials. // Periodica Mathematica Hungarica. 45 (2002) , 1-2; 21-33 (journal article).
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  Nonscientific papers in other journals
 

1. Dujella, Andrej.
Vigenere Cipher. // Math.e. 1 (2004) , 1; - (journal article). URL link to work

2. Gusić, Ivica.
Why the complex numbers were introduced. // Math.e : hrvatski matematički elektronski časopis. 1 (2004) , 1; 0-0 (journal article). URL link to work
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  Abstracts in Book of abstracts
 

1. Dujella, Andrej.
High rank elliptic curves with prescribed torsion group // NyirCrypt.
Debrecen : University of Debrecen, 2006. 5-5 (lecture,international peer-review,abstract,scientific).

2. Filipin, Alan; Dujella, Andrej; Fuchs, Clemens.
On the D(-1)-quadruple conjecture // Canadian Number Theory Association IX Meeting.
Vancouver : University of British Columbia, 2006. 38-38 (lecture,international peer-review,abstract,scientific).

3. Dujella, Andrej.
Asymptotic estimates for the number of Diophantine m-tuples // XXIV-iemes Journees Arithmetiques.
Marseille : Universite de Provence, 2005. 26-26 (lecture,international peer-review,abstract,scientific).

4. Dujella, Andrej.
Diophantine m-tuples and connections with eliptic curves // Mathematik 2005 / Kadunz, G. ; More, W., editor(s).
Klagenfurt, 2005. 81-81 (invited talk,international peer-review,abstract,scientific).

5. Gusić, Ivica.
On equation f(x)=g(y) // Mathematik 2005 / Kadunz, G. ; More, W., editor(s).
Klagenfurt, 2005. 190-190 (lecture,international peer-review,abstract,scientific).

6. Jadrijević, Borka.
On Some Parametric Families of Quartic Thue Equations and a Related Familiy of Relative Thue Equations // Mathematik 2005 / Kadunz, G. ; More, W., editor(s).
Klagenfurt, 2005. 191-191 (lecture,international peer-review,abstract,scientific).

7. Jadrijević, Borka; Ziegler, Volker.
system of relative Pellian equations and a related family of relative Thue equations // XXIV-iemes Journees Arithmetiques.
Marseille : Universite de Provence, 2005. 36-36 (lecture,international peer-review,abstract,scientific).

8. Dujella, Andrej.
On a problem of Diophantus and Euler // Third Croatian Congress of Mathematics.
Split : Hrvatsko matematičko društvo, 2004. 30-30 (lecture,international peer-review,abstract,scientific).

9. Dujella, Andrej.
Newton's approximants and continued fractions // Number Theoretic Algorithms and Related Topics / Drmota, M. ; Larcher, G. ; Tichy, R. ; Winkler, R., editor(s).
Strobl : Technische Universitat Wien, 2004. 8-9 (invited talk,abstract,scientific).

10. Jadrijević, Borka.
A two-parametric family of quartic Thue equations and related system of Pellian equations // Third Croatian Congress of Mathematics.
Split : Hrvatsko matematičko društvo, 2004. 34-34 (lecture,international peer-review,abstract,scientific).

11. Jadrijević, Borka.
A family of quartic Thue inequalities // Number Theoretic Algorithms and Related Topics / Drmota, M. ; Larcher, G. ; Tichy, R. ; Winkler, R., editor(s).
Strobl : Technische Universitat Graz, 2004. 12-13 (lecture,abstract,scientific).

12. Dujella, Andrej.
Continued fractions and RSA with small secret exponent // TATRACRYPT 2003 / Grošek, Otokar ; Nemoga, Karol, editor(s).
Bratislava : Slovak University of Technology, 2003. 4-4 (lecture,international peer-review,abstract,scientific).

13. Dujella, Andrej.
On Diophantine quintuple conjecture // XXIII Journees Arithmetiques Graz 2003.
Graz : Karl-Franzens-Universitat Graz, 2003. 41-41 (lecture,international peer-review,abstract,scientific).

14. Jadrijević, Borka.
Parametric families of quartic Thue equations and inequalities // XXIII Journees Arithmetiques Graz 2003.
Graz : Karl-Franzens-Universitat Graz, 2003. 49-49 (lecture,international peer-review,abstract,scientific).

15. Dujella, Andrej.
Construction of high-rank elliptic curves with non-trivial torsion group // Second Central European Conference on Cryptography HAJDUCRYPT'02 / Petho, Attila, editor(s).
Debrecin : University of Debrecen, 2002. 6-6 (lecture,international peer-review,abstract,scientific).
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  Unpublished papers
 

1. Dujella, Andrej.
Diophantine m-tuples // .
(invited talk,unpublished,scientific).

2. Dujella, Andrej.
Construction of elliptic curves over Q with large rank // .
(invited talk,international peer-review,unpublished,scientific).
Vrh
 
  Dissertations
 

1. Filipin, Alan.
Systems of Pellian Equations and the Problem of Extension of Some Diophantine Triples / doctoral thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 02.11. 2006, 99 pages. Mentor: Dujella, Andrej.

2. Franušić, Zrinka.
Diophantine quadruples in quadratic fields / doctoral thesis.
Zagreb : Prirodoslovno matematički fakultet, 29.09. 2005, 115 pages. Mentor: Dujella, Andrej.

3. Jadrijević, Borka.
Twoparametric family of quartic Thue equations / doctoral thesis.
Zagreb : PMF - Matematički odjel, 31.10. 2001., 100 pages. Mentor: Dujella, Andrej.
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  Master thesis
 

1. Jurasić, Ana.
Diophantine Equations over Function Fields / pre-Bologna master thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 11.12. 2006, 115 pages. Mentor: Dujella, Andrej.

2. Tadić, Petra.
Methods for computing the rank of elliptic curves over Q(T) / pre-Bologna master thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 27.09. 2006, 129 pages. Mentor: Dujella, Andrej.

3. Kopčinović, Danijel.
Discrete logarithm problem for elliptic curves / pre-Bologna master thesis.
Zagreb : PMF - Matematički odjel, 02.03. 2005., 127 pages. Mentor: Dujella, Andrej.

4. Filipin, Alan.
Application of LLL-algorithm in solving Diophantine equations / pre-Bologna master thesis.
Zagreb : PMF - Matematički odjel, 12.07. 2004., 105 pages. Mentor: Dujella, Andrej.

5. Ibrahimpašić, Bernadin.
Mathematical Basis of Public-Key Cryptography / pre-Bologna master thesis.
Sarajevo : Prirodno-matematički fakultet, 31.08. 2004, 127 pages. Mentor: Dujella, Andrej.
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  Graduation thesis
 

1. Čulo, Nina.
Algebraic Numbers / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 28.06. 2006., 35 pages. Mentor: Dujella, Andrej.

2. Flego, Valentina.
PGP - Pretty Good Privacy / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 12.07. 2006., 48 pages. Mentor: Dujella, Andrej.

3. Kantoci, Tanja.
Modern Block Ciphers / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 20.02. 2006., 42 pages. Mentor: Dujella, Andrej.

4. Matanović, Josip.
Steganography: Hiding Information in Images / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 15.05. 2006., 40 pages. Mentor: Dujella, Andrej.

5. Miletić, Marina.
Transposition Ciphers / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 24.02. 2006, 37 pages. Mentor: Dujella, Andrej.

6. Odak, Mihaela.
Error-correcting Codes and McEliece Cryptosystem / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 06.02. 2006, 52 pages. Mentor: Dujella, Andrej.

7. Radulović, Maja.
Markov Chain / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 02.05. 2006, 46 pages. Mentor: Dujella, Andrej.

8. Šeremet, Marko.
Algorithms for Large-Integer Multiplications / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 12.06. 2006, 46 pages. Mentor: Dujella, Andrej.

9. Škarijot, Danijela.
Digital Watermarking / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 05.05. 2006, 37 pages. Mentor: Dujella, Andrej.

10. Skelin, Branka.
Elliptic Curves and Elliptic Functions / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 04.12. 2006, 41 pages. Mentor: Dujella, Andrej.

11. Bogunović, Helena.
Arithmetic Functions / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 07.11. 2005., 68 pages. Mentor: Dujella, Andrej.

12. Kalina, Tonći.
Internet Security and SSL Protocol / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 14.07. 2005., 35 pages. Mentor: Dujella, Andrej.

13. Mokrović, Romana.
Topological Convex Structures / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 30.11. 2005, 40 pages. Mentor: Dujella, Andrej.

14. Pejković, Tomislav.
Roth's Theorem / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno matematički fakultet - Matematički odjel, 21.11. 2005., 64 pages. Mentor: Dujella, Andrej.

15. Tomić, Ana-Marija.
Digital Signature and Digital Money / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 27.06. 2005, 46 pages. Mentor: Dujella, Andrej.

16. Zeljković, Sanja.
Steganography / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 30.03. 2005, 36 pages. Mentor: Dujella, Andrej.

17. Blažević, Irena.
RC6 Cryptosystem / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 26.04. 2004., 67 pages. Mentor: Dujella, Andrej.

18. Dragović, Helena.
History of Cryptography / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 13.07. 2004., 58 pages. Mentor: Dujella, Andrej.

19. Pačić, Irena.
Shannon's Theory / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 26.02. 2004, 40 pages. Mentor: Dujella, Andrej.

20. Vrban, Ana.
Monoalphabetic Substitution Ciphers / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 15.10. 2004, 36 pages. Mentor: Dujella, Andrej.

21. Buha, Sabrina.
Fermat's Little Theorem and Its Consequences / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 20.02. 2003., 36 pages. Mentor: Dujella, Andrej.

22. Ezgeta, Mia.
Primality Testing / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 28.02. 2003., 40 pages. Mentor: Dujella, Andrej.

23. Gabaj, Mirela.
Mersenne Numbers and Perfect Numbers / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 08.12. 2003., 38 pages. Mentor: Dujella, Andrej.

24. Gregurić, Jadranka.
DES Cryptosystem / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 10.09. 2003., 40 pages. Mentor: Dujella, Andrej.

25. Jozić, Aneta.
Congruences of Integers and Polynomials / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 15.10. 2003., 45 pages. Mentor: Dujella, Andrej.

26. Kazalicki, Matija.
Modular functions and complex multiplication of elliptic curves / pre-Bologna graduate thesis.
Zagreb : PMF - Matematički odjel, 19.12. 2003., 55 pages. Mentor: Dujella, Andrej.

27. Korunek, Ana.
Statistical Properties of Arithmetic Functions / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 29.10. 2003., 32 pages. Mentor: Dujella, Andrej.

28. Kundić, Ana.
Knapsack Problem and Applications in Cryptography / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 19.02. 2003., 80 pages. Mentor: Dujella, Andrej.

29. Milun, Jelena.
Continued Fractions and Their Applications / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 19.02. 2003, 42 pages. Mentor: Dujella, Andrej.

30. Petričević, Vinko.
Congruent numbers and elliptic curves / pre-Bologna graduate thesis.
Zagreb : PMF - Matematički odjel, 13.10. 2003., 37 pages. Mentor: Dujella, Andrej.

31. Polić, Narcisa.
Zero-knowledge Proofs / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet, 27.03. 2003, 35 pages. Mentor: Dujella, Andrej.

32. Soldo, Ružica.
Kneser's Theorem / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 31.03. 2003, 36 pages. Mentor: Dujella, Andrej.

33. Tadić, Petra.
Mordell's theorem / pre-Bologna graduate thesis.
Zagreb : PMF - Matematički odjel, 07.01. 2003, 51 pages. Mentor: Dujella, Andrej.

34. Buntak, Robert.
Diffie-Hellman Key Distribution Protocol / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 23.09. 2002., 39 pages. Mentor: Dujella, Andrej.

35. Krulić, Tamara.
Hash Functions in Cryptography / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 09.12. 2002., 30 pages. Mentor: Dujella, Andrej.

36. Matijević, Mario.
Discrete Logarithm Problem / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matemtički fakultet - Matematički odjel, 25.11. 2002, 40 pages. Mentor: Dujella, Andrej.

37. Ozvačić, Dalibor.
Fibonacci Numbers and the Golden Section / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 29.11. 2002, 32 pages. Mentor: Dujella, Andrej.

38. Sesjak, Tajana.
Polyalphabetic Ciphers / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 04.10. 2002, 46 pages. Mentor: Dujella, Andrej.

39. Terzić, Dubravka.
Primality Tests / pre-Bologna graduate thesis.
Zagreb : Prirodoslovno-matematički fakultet - Matematički odjel, 11.11. 2002, 40 pages. Mentor: Dujella, Andrej.
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