Publications of Andrej Dujella

(with papers in pdf format)


  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 and A. Jurasic, On the size of sets in a polynomial variant of a problem of Diophantus, Int. J. Number Theory 6 (2010), 1449-1471.

  67. A. Dujella, On Hall's conjecture, Acta Arith. 147 (2011), 397-402.

  68. A. Dujella, B. Ibrahimpasic and B. Jadrijevic, Solving a family of quartic Thue inequalities using continued fractions, Rocky Mountain J. Math. 41 (2011), 1173-1182.

  69. Y. Bugeaud and A. Dujella, Root separation for irreducible integer polynomials, Bull. Lond. Math. Soc. 43 (2011), 1239-1244.

  70. A. Dujella and T. Pejkovic, Root separation for reducible monic quartics, Rend. Semin. Mat. Univ. Padova 126 (2011), 63-72.

  71. A. Bérczes, A. Dujella, L. Hajdu and F. Luca, On the size of sets whose elements have perfect power n-shifted products, Publ. Math. Debrecen 79 (2011), 325-339.

  72. A. Dujella and A. Jurasic, Some Diophantine triples and quadruples for quadratic polynomials, J. Comb. Number Theory 3(2) (2011), 123-141.

  73. A. Dujella and C. Fuchs, On a problem of Diophantus for rationals, J. Number Theory 132 (2012), 2075-2083.

  74. A. Dujella and F. Luca, On the sum of two divisors of (n2 + 1)/2, Period. Math. Hungar. 65 (2012), 83-96.

  75. A. Dujella, K. Gyory and A. Pinter, On power values of pyramidal numbers, I, Acta Arith. 155 (2012), 217-226.

  76. S. Diaz Alvarado, A. Dujella and F. Luca, On a conjecture regarding balancing with powers of Fibonacci numbers, Integers 12A (2012), #A2. (29pp)

  77. A. Dujella and F. Najman, Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization, Period. Math. Hungar. 65 (2012), 193-203.

  78. J. Aguirre, A. Dujella and J. C. Peral, On the rank of elliptic curves coming from rational Diophantine triples, Rocky Mountain J. Math. 42 (2012), 1759-1776.

  79. A. Dujella and F. Luca, On a variation of a congruence of Subbarao, J. Aust. Math. Soc. 93 (2012), 85-90.

  80. A. Dujella and J. C. Peral, Elliptic curves and triangles with three rational medians, J. Number Theory 133 (2013), 2083-2091.

  81. A. Dujella and C. Elsholtz, Sumsets being squares, Acta Math. Hungar. 141 (2013), 353-357.

  82. J. Aguirre, A. Dujella and J. C. Peral, Arithmetic progressions and Pellian equations, Publ. Math. Debrecen 83 (2013), 683-695.

  83. A. Dujella and N. Saradha, Diophantine m-tuples with elements in arithmetic progressions, Indag. Math. (N.S.) 25 (2014), 131-136.

  84. A. Bérczes, A. Dujella and L. Hajdu, Some Diophantine properties of the sequence of S-units, J. Number Theory 138 (2014), 48-68.

  85. Y. Bugeaud and A. Dujella, Root separation for reducible integer polynomials, Acta Arith. 162 (2014), 393-403.

  86. A. Dujella and M. Mikic, On the torsion group of elliptic curves induced by D(4)-triples, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 22 (2014), 79-90.

  87. J. Bosman, P. Bruin, A. Dujella and F. Najman, Ranks of elliptic curves with prescribed torsion over number fields, Int. Math. Res. Not. IMRN 2014 (11) (2014), 2885-2923.

  88. A. Dujella and J. C. Peral, High rank elliptic curves with torsion Z/2Z × Z/4Z induced by Diophantine triples, LMS J. Comput. Math. 17 (2014), 282-288.

  89. J. Aguirre, A. Dujella, M. Jukic Bokun and J. C. Peral, High rank elliptic curves with prescribed torsion group over quadratic fields, Period. Math. Hungar. 68 (2014), 222-230.

  90. A. Dujella, F. Najman, N. Saradha and T. N. Shorey, Products of three factorials, Publ. Math. Debrecen 85 (2014), 123-130.

  91. A. Dujella, I. Gusic and L. Lasic, On quadratic twists of elliptic curves y2 = x(x - 1)(x - λ), Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 18 (2014), 27-34.

  92. A. Dujella and J. C. Peral, Elliptic curves coming from Heron triangles, Rocky Mountain J. Math. 44 (2014), 1145-1160.

  93. A. S. Janfada, S. Salami, A. Dujella and J. C. Peral, On the high rank π/3 and 2π/3 - congruent number elliptic curves, Rocky Mountain J. Math. 44 (2014), 1867-1880.

  94. B. Peker, A. Dujella and S. Cenberci, The non-extensibility of D(-2k+1)-triples {1, k2, k2+2k-1}, Miskolc Math. Notes 16 (2015), 385-390.

  95. A. Dujella and J. C. Peral, Elliptic curves with torsion group Z/8Z or Z/2Z × Z/6Z, in Trends in Number Theory, Contemp. Math. 649 (2015), 47-62.

  96. A Dujella, I. Gusic and P. Tadic, The rank and generators of Kihara's elliptic curve with torsion Z/4Z over Q(t), Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), 105-109.

  97. A. Bérczes, A. Dujella, L. Hajdu and S. Tengely, Finiteness results for F-Diophantine sets, Monatsh. Math. 180 (2016), 469-484.

  98. A. Dujella, What is ... a Diophantine m-tuple?, Notices Amer. Math. Soc. 63 (2016), 772-774

  99. A Dujella, J. C. Peral and P. Tadic, Elliptic curves with torsion group Z/6Z, Glas. Mat. Ser. III 51 (2016), 321-333.

  100. A. Dujella, M. Kazalicki, M. Mikic and M. Szikszai, There are infinitely many rational Diophantine sextuples, Int. Math. Res. Not. IMRN 2017 (2) (2017), 490-508.

  101. A. Dujella and M. Kazalicki, More on Diophantine sextuples, in Number Theory - Diophantine problems, uniform distribution and applications, Festschrift in honour of Robert F. Tichy's 60th birthday (C. Elsholtz, P. Grabner, Eds.), Springer-Verlag, Berlin, 2017, pp. 227-235.

  102. A. Dujella, M. Jukic Bokun and I. Soldo, On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 111 (2017), 1177-1185.

  103. A. Dujella and T. Pejkovic, Root separation for reducible monic polynomials of odd degree, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 21 (2017), 21-27.

  104. Y. Bugeaud, A. Dujella, T. Pejkovic and B. Salvy, Absolute real root separation, Amer. Math. Monthly, to appear. (9pp)

  105. N. Adzaga, A. Dujella, D. Kreso and P. Tadic, Triples which are D(n)-sets for several n's, J. Number Theory, to appear. (12pp)

  106. A. Dujella and M. Kazalicki, Diophantine m-tuples in finite fields and modular forms, preprint. (26pp)

  107. A. Dujella, M. Jukic Bokun and I. Soldo, A Pellian equation with primes and applications to D(-1)-quadruples, preprint. (14pp)

  108. A. Dujella and F. Luca, On fundamental units of class number one quadratic fields, preprint. (7pp)


Publications in Croatian

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Diophantine m-tuples page


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