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. Petho, 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. Petho, 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, Int. Math. Res. Not. 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. Petho; 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 124 (2017), 930-936.

  105. N. Adzaga, A. Dujella, D. Kreso and P. Tadic, Triples which are D(n)-sets for several n's, J. Number Theory 184 (2018), 330-341.

  106. A. Dujella, I. Gusic, V. Petricevic and P. Tadic, Strong Eulerian triples, Glas. Mat. Ser. III 53 (2018), 33-42.

  107. N. Adzaga, A. Dujella, D. Kreso and P. Tadic, On Diophantine m-tuples and D(n)-sets, RIMS Kokyuroku 2092 (2018), 130-137.

  108. A. Dujella and J. C. Peral, Elliptic curves induced by Diophantine triples, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 113 (2019), 791-806.

  109. A. Dujella, M. Jukic Bokun and I. Soldo, A Pellian equation with primes and applications to D(-1)-quadruples, Bull. Malays. Math. Sci. Soc. 42 (2019), 2915-2926.

  110. A. Bérczes, A. Dujella, L. Hajdu, N. Saradha and R. Tijdeman, Products of factorials which are powers, Acta Arith. 190 (2019), 339-350.

  111. A. Dujella, M. Kazalicki and V. Petricevic, Rational Diophantine sextuples with square denominators, J. Number Theory 205 (2019), 340-346.

  112. A. Dujella and F. Luca, On fundamental units of real quadratic fields of class number 1, Arch. Math. (Basel) 113 (2019), 349-353.

  113. A. Dujella and V. Petricevic, On the largest element in D(n)-quadruples, Indag. Math. (N.S.) 30 (2019), 1079-1086.

  114. A. Dujella and V. Petricevic, Diophantine quadruples with the properties D(n1) and D(n2), Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 114 (2020), Article 21, (9pp)

  115. A. Dujella, M. Paganin and M. Sadek, Strong rational Diophantine D(q)-triples, Indag. Math. (N.S.) 31 (2020), 505-511.

  116. A. Dujella and V. Petricevic, Doubly regular Diophantine quadruples, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 114 (2020), Article 189, (8pp)

  117. A. Dujella and M. Mikic, Rank zero elliptic curves induced by rational Diophantine triples, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 24 (2020), 29-37.

  118. A. Dujella and J. C. Peral, High rank elliptic curves induced by rational Diophantine triples, Glas. Mat. Ser. III 55 (2020), 237-252.

  119. A. Dujella, M. Kazalicki and V. Petricevic, Rational Diophantine sextuples containing two regular quadruples and one regular quintuple, Acta Mathematica Spalatensia 1 (2021), 19-27.

  120. A. Dujella and M. Kazalicki, Diophantine m-tuples in finite fields and modular forms, Res. Number Theory 7 (2021), Article number 3, (24pp)

  121. M. Cipu, A. Dujella and Y. Fujita, Diophantine triples with largest two elements in common, Period. Math. Hungar. 82 (2021), 56-68.

  122. A. Dujella and J. C. Peral, Construction of high rank elliptic curves, J. Geom. Anal. 31 (2021), 6698-6724.

  123. A. Dujella, M. Kazalicki and J. C. Peral, Elliptic curves with torsion groups Z/8Z and Z/2Z × Z/6Z, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 115 (2021), Article 169, (24pp)

  124. A. Dujella, M. Kazalicki and V. Petricevic, D(n)-quintuples with square elements, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 115 (2021), Article 172, (10pp)

  125. A. Dujella and G. Soydan, On elliptic curves induced by rational Diophantine quadruples, Proc. Japan Acad. Ser. A Math. Sci. 98 (2022), 1-6.

  126. M. Cipu, A. Dujella and Y. Fujita, Extensions of a Diophantine triple by adjoining smaller elements, Mediterr. J. Math. 19 (2022), Article 187, (20pp)

  127. Y. Bugeaud, A. Dujella, W. Fang, T. Pejkovic and B. Salvy, Absolute root separation, Experiment. Math. 31 (2022), 806-813.

  128. A. Dujella, Z. Franusic and V. Petricevic, Formulas for Diophantine quintuples containing two pairs of conjugates in some quadratic fields, Period. Math. Hungar. 85 (2022), 303-311.

  129. A. Dujella, K. Gyory, P. Michaud-Jacobs and A. Pinter, On power values of pyramidal numbers, II, Acta Arith. 208 (2023), 199-213.

  130. A. Dujella, High-rank elliptic curves with given torsion group and some applications, Number-Theoretic Methods in Cryptology (M. Grzeskowiak, J. Pieprzyk, J. Pomykala, ed.), Banach Center Publications 126, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2023, pp. 9-26.

  131. A. Dujella and J. C. Peral, An elliptic curve over Q(u) with torsion Z/4Z and rank 6, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 28 (2024), 185-192.

  132. M. Cipu, A. Dujella and Y. Fujita, Extensions of a Diophantine triple by adjoining smaller elements II, Period. Math. Hungar. 89 (2024), 54-60.

  133. A. Dujella, Triples, quadruples and quintuples which are D(n)-sets for several n's, in: Class Groups of Number Fields and Related Topics. ICCGNERT 2021, ICCGNERT 2022 (K. Chakraborty, A. Hoque and P. P. Pandey, Eds.), Springer, Singapore, 2024, pp. 77-92.

  134. N. Adzaga, G. Drazic, A. Dujella and A. Petho, Asymptotics of D(q)-pairs and triples via L-functions of Dirichlet characters, Ramanujan J., to appear. (20pp)

  135. A. Dujella, M. Kazalicki and V. Petricevic, Rational Diophantine sextuples with strong pair, preprint. (9pp)

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