Publications of Andrej Dujella

(with papers in dvi format; for paper in pdf format see here)


  1. A. Dujella, Generalization of a problem of Diophantus, Acta Arith. 65 (1993), 15-27.

  2. A. Dujella, Diophantine quadruples for squares of Fibonacci and Lucas numbers, Portugaliae Math. 52 (1995), 305-318.

  3. A. Dujella, Generalized Fibonacci numbers and the problem of Diophantus, Fibonacci Quart. 34 (1996), 164-175.

  4. A. Dujella, Some polynomial formulas for Diophantine quadruples, Grazer Math. Ber. 328 (1996), 25-30.

  5. A. Dujella, On Diophantine quintuples, Acta Arith. 81 (1997), 69-79.

  6. A. Dujella, The problem of Diophantus and Davenport for Gaussian integers, Glas. Mat. Ser. III 32 (1997), 1-10.

  7. A. Dujella, The problem of the extension of a parametric family of Diophantine triples, Publ. Math. Debrecen, 51 (1997), 311-322.

  8. A. Dujella, The problem of Diophantus and Davenport, Math. Commun. 2 (1997), 153-160.

  9. A. Dujella, On the exceptional set in the problem of Diophantus and Davenport, Application of Fibonacci Numbers, Vol. 7 (G. E. Bergum, A. N. Philippou, A. F. Horadam, eds.), Kluwer, Dordrecht, 1998, pp. 69-76.

  10. A. Dujella, A problem of Diophantus and Pell numbers, Application of Fibonacci Numbers, Vol. 7 (G. E. Bergum, A. N. Philippou, A. F. Horadam, eds.), Kluwer, Dordrecht, 1998, pp. 61-68.

  11. A. Dujella, A problem of Diophantus and Dickson's conjecture, Number Theory, Diophantine, Computational and Algebraic Aspects (K. Gyory, A. Petho, V. T. Sos, eds.), Walter de Gruyter, Berlin, 1998, pp. 147-156.

  12. A. Dujella, Some estimates of the number of Diophantine quadruples, Publ. Math. Debrecen 53 (1998), 177-189.

  13. A. Dujella and A. Pethoe, A generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser. (2), 49 (1998), 291-306.

  14. A. Dujella, Complete solution of a family of simultaneous Pellian equations, Acta Math. Inform. Univ. Ostraviensis 6 (1998), 59-67.

  15. A. Dujella, Diophantine quadruples and quintuples modulo 4, Notes Number Theory Discrete Math. 4 (1998), 160-164.

  16. A. Dujella, A bijective proof of Riordan's theorem on powers of Fibonacci numbers, Discrete Math. 199 (1999), 217-220.

  17. A. Dujella, A proof of the Hoggatt-Bergum conjecture, Proc. Amer. Math. Soc. 127 (1999), 1999-2005.

  18. A. Dujella, An extension of an old problem of Diophantus and Euler, Fibonacci Quart. 37 (1999), 312-314.

  19. A. Dujella, Diophantine triples and construction of high-rank elliptic curves over Q with three non-trivial 2-torsion points, Rocky Mountain J. Math. 30 (2000), 157-164.

  20. A. Dujella, A note on Diophantine quintuples, Algebraic Number Theory and Diophantine Analysis (F. Halter-Koch, R. F. Tichy, eds.), Walter de Gruyter, Berlin, 2000, pp. 123-127.

  21. A. Dujella, A parametric family of elliptic curves, Acta Arith. 94 (2000), 87-101; extended version. (41pp)

  22. A. Dujella, Irregular Diophantine m-tuples and elliptic curves of high rank, Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), 66-67.

  23. A. Dujella and A. Pethoe, Integer points on a family of elliptic curves, Publ. Math. Debrecen 56 (2000), 321-335.

  24. A. Dujella, Newton's formula and continued fraction expansion of sqrt(d), Experiment. Math. 10 (2001), 125-131.

  25. A. Dujella, An absolute bound for the size of Diophantine m-tuples, J. Number Theory 89 (2001), 126-150.

  26. A. Dujella, Diophantine m-tuples and elliptic curves, J. Theor. Nombres Bordeaux 13 (2001), 111-124.

  27. A. Dujella and R. F. Tichy, Diophantine equations for second order recursive sequences of polynomials, Quart. J. Math. Oxford Ser. (2) 52 (2001), 161-169.

  28. A. Dujella and B. Jadrijevic, A parametric family of quartic Thue equations, Acta Arith. 101 (2002), 159-170.

  29. A. Dujella, On the size of Diophantine m-tuples, Math. Proc. Cambridge Philos. Soc. 132 (2002), 23-33.

  30. A. Dujella, An extension of an old problem of Diophantus and Euler. II, Fibonacci Quart. 40 (2002), 118-123.

  31. M. N. Deshpande and A. Dujella, An interesting property of a recurrence related to the Fibonacci sequence, Fibonacci Quart. 40 (2002), 157-160.

  32. A. Dujella, An example of elliptic curve over Q with rank equal to 15, Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), 109-111.

  33. A. Dujella, C. Fuchs and R. F. Tichy, Diophantine m-tuples for linear polynomials, Period. Math. Hungar. 45 (2002), 21-33.

  34. Y. Bugeaud and A. Dujella, On a problem of Diophantus for higher powers, Math. Proc. Cambridge Philos. Soc. 135 (2003), 1-10.

  35. A. Dujella and C. Fuchs, A polynomial variant of a problem of Diophantus and Euler, Rocky Mountain J. Math. 33 (2003), 797-811.

  36. A. Dujella and B. Jadrijevic, A family of quartic Thue inequalities, Acta Arith. 111 (2004), 61-76.

  37. A. Dujella, There are only finitely many Diophantine quintuples, J. Reine Angew. Math. 566 (2004), 183-214.

  38. A. Dujella and C. Fuchs, Complete solution of the polynomial version of a problem of Diophantus, J. Number Theory 106 (2004), 326-344.

  39. A. Dujella, Bounds for the size of sets with the property D(n), Glas. Mat. Ser. III 39 (2004), 199-205.

  40. A. Dujella, Diophantine quadruples and Fibonacci numbers, Bulletin of Kerala Mathematical Association 1 (2004), 133-147.

  41. A. Dujella, Continued fractions and RSA with small secret exponent, Tatra Mt. Math. Publ. 29 (2004), 101-112.

  42. A. Dujella and C. Fuchs, Complete solution of a problem of Diophantus and Euler, J. London Math. Soc. 71 (2005), 33-52.

  43. A. Dujella and V. Petricevic, Square roots with many good approximants, Integers 5(3) (2005), #A6. (13pp)

  44. A. Dujella and A. M. S. Ramasamy, Fibonacci numbers and sets with the property D(4), Bull. Belg. Math. Soc. Simon Stevin 12 (2005), 401-412.

  45. A. Dujella and F. Luca, Diophantine m-tuples for primes, Intern. Math. Research Notices 47 (2005), 2913-2940.

  46. A. Dujella, I. Gusic and R. F. Tichy, On the indecomposability of polynomials, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 214 (2005), 81-88.

  47. A. Dujella and I. Gusic, Indecomposability of polynomials and related Diophantine equations, Q. J. Math. (Oxford) 57 (2006), 193-201.

  48. A. Dujella, C. Fuchs and P. G. Walsh, Diophantine m-tuples for linear polynomials. II. Equal degrees, J. Number Theory 120 (2006), 213-228.

  49. A. Dujella and F. Luca, On a problem of Diophantus with polynomials, Rocky Mountain J. Math. 37 (2007), 131-157.

  50. A. Dujella and Z. Franusic, On differences of two squares in some quadratic fields, Rocky Mountain J. Math. 37 (2007), 429-453.

  51. A. Dujella, On Mordell-Weil groups of elliptic curves induced by Diophantine triples, Glas. Mat. Ser. III 42 (2007), 3-18.

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

  53. Y. Bugeaud, A. Dujella and M. Mignotte, On the family of Diophantine triples {k - 1, k + 1, 16k3 - 4k}, Glasgow Math. J. 49 (2007), 333-344.

  54. A. Dujella and I. Gusic, Decomposition of a recursive family of polynomials, Monatsh. Math. 152 (2007), 97-104.

  55. A. Dujella, On the number of Diophantine m-tuples, Ramanujan J. 15 (2008), 37-46.

  56. A. Dujella, Conjectures and results on the size and number of Diophantine tuples, Diophantine Analysis and Related Fields (DARF 2007/2008), AIP Conf. Proc. 976 (T. Komatsu, ed.), Amer. Inst. Phys., Melville, NY, 2008, pp. 58-61.

  57. A. Dujella, C. Fuchs and F. Luca, A polynomial variant of a problem of Diophantus for pure powers, Int. J. Number Theory 4 (2008), 57-71.

  58. A. Dujella and V. Petricevic, Strong Diophantine triples, Experiment. Math. 17 (2008), 83-89.

  59. A. Dujella, A. Pethoe and P. Tadic, On arithmetic progressions on Pellian equations, Acta Math. Hungar. 120 (2008), 29-38.

  60. A. Dujella and B. Ibrahimpasic, On Worley's theorem in Diophantine approximations, Ann. Math. Inform. 35 (2008), 61-73.

  61. A. Dujella, Rational Diophantine sextuples with mixed signs, Proc. Japan Acad. Ser. A Math. Sci. 85 (2009), 27-30.

  62. A. Dujella, A variant of Wiener's attack on RSA, Computing 85 (2009), 77-83.

  63. A. Dujella, A. S. Janfada and S. Salami, A search for high rank congruent number elliptic curves, J. Integer Seq. 12 (2009), Article 09.5.8 (11pp)

  64. A. Dujella and I. Soldo, Diophantine quadruples in Z[√-2], An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 18 (2010), 81-98.

  65. A. Dujella and M. Jukic Bokun, On the rank of elliptic curves over Q(i) with torsion group Z/4Z × Z/4Z, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), 93-96.

  66. A. Dujella, B. Ibrahimpasic and B. Jadrijevic, Solving a family of quartic Thue inequalities using continued fractions, Rocky Mountain J. Math., to appear. (9pp)

  67. A. Dujella and A. Jurasic, On the size of sets in a polynomial variant of a problem of Diophantus, Int. J. Number Theory, to appear. (20pp)

  68. J. Aguirre, A. Dujella and J. C. Peral, On the rank of elliptic curves coming from rational Diophantine triples, Rocky Mountain J. Math., to appear. (13pp)

  69. A. Dujella, On Hall's conjecture, Acta Arith., to appear. (7pp)

  70. A. Dujella and F. Luca, On the sum of two divisors of (n2 + 1)/2, preprint. (16pp)

  71. Y. Bugeaud and A. Dujella, Root separation for irreducible integer polynomials, preprint. (7 pp)

Publications in Croatian

Lectures on conferences

Invited lectures

Diophantine m-tuples page

Andrej Dujella home page