All Stories

  1. An elliptic curve over Q(u) with torsion Z/4Z and rank 6

    Article • Rad Hrvatske akademije znanosti i umjetnosti Matematičke znanosti, January 2024, Croatian Academy of Sciences and Arts

    Professor Andrej Dujella

  2. Extensions of a Diophantine triple by adjoining smaller elements II

    Article • Periodica Mathematica Hungarica, December 2023, Springer Science + Business Media

    Professor Andrej Dujella

  3. High-rank elliptic curves with given torsion group and some applications

    Article • Banach Center Publications, January 2023, Institute of Mathematics, Polish Academy of Sciences

    Professor Andrej Dujella

  4. Extensions of a Diophantine Triple by Adjoining Smaller Elements

    Article • Mediterranean Journal of Mathematics, July 2022, Springer Science + Business Media

    Professor Andrej Dujella

  5. On elliptic curves induced by rational Diophantine quadruples

    Article • Proceedings of the Japan Academy Series A Mathematical Sciences, January 2022, Project Euclid

    Professor Andrej Dujella

  6. Formulas for Diophantine quintuples containing two pairs of conjugates in some quadratic fields

    Article • Periodica Mathematica Hungarica, January 2022, Springer Science + Business Media

    Professor Andrej Dujella

  7. D(n)-quintuples with square elements

    Article • Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas, August 2021, Springer Science + Business Media

    Professor Andrej Dujella

  8. Elliptic curves with torsion groups $${ \mathbb {Z}}/ 8 {\mathbb {Z} } $$ and $${ \mathbb {Z}}/ 2 {\mathbb {Z}} \times {\mathbb {Z}}/ 6 {\mathbb {Z}}$$

    Article • Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas, August 2021, Springer Science + Business Media

    Professor Andrej Dujella

  9. Rational Diophantine sextuples containing two regular quadruples and one regular quintuple

    Article • Acta mathematica Spalatensia, January 2021, Faculty of Science, University of Split

    Professor Andrej Dujella

  10. Diophantine m-tuples in finite fields and modular forms

    Article • Research in Number Theory, January 2021, Springer Science + Business Media

    Professor Andrej Dujella

  11. High rank elliptic curves induced by rational Diophantine triples

    Article • Glasnik Matematicki, December 2020, University of Zagreb, Department of Mathematics

    Professor Andrej Dujella

  12. Doubly regular Diophantine quadruples

    Article • Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas, August 2020, Springer Science + Business Media

    Professor Andrej Dujella

  13. Strong rational Diophantine D(q)

    Article • Indagationes Mathematicae, May 2020, Elsevier

    Professor Andrej Dujella

  14. Diophantine triples with largest two elements in common

    Article • Periodica Mathematica Hungarica, March 2020, Springer Science + Business Media

    Professor Andrej Dujella

  15. Construction of High Rank Elliptic Curves

    Article • Journal of Geometric Analysis, March 2020, Springer Science + Business Media

    Professor Andrej Dujella

  16. Rank zero elliptic curves induced by rational Diophantine triples

    Article • Rad Hrvatske akademije znanosti i umjetnosti Matematičke znanosti, January 2020, Croatian Academy of Sciences and Arts

    Professor Andrej Dujella

  17. Absolute Root Separation

    Article • Experimental Mathematics, December 2019, Taylor & Francis

    Professor Andrej Dujella

  18. Diophantine quadruples with the properties $$D(n_1)$$ and $$D(n_2)$$

    Article • Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas, December 2019, Springer Science + Business Media

    Professor Andrej Dujella

  19. Rational Diophantine sextuples with square denominators

    Article • Journal of Number Theory, December 2019, Elsevier

    Professor Andrej Dujella

  20. On the largest element in D(n)

    Article • Indagationes Mathematicae, November 2019, Elsevier

    Professor Andrej Dujella

  21. On fundamental units of real quadratic fields of class number 1

    Article • Archiv der Mathematik, June 2019, Springer Science + Business Media

    Professor Andrej Dujella

  22. Products of factorials which are powers

    Article • Acta Arithmetica, January 2019, Institute of Mathematics, Polish Academy of Sciences

    Professor Andrej Dujella

  23. Strong Eulerian triples

    Article • Glasnik Matematicki, June 2018, University of Zagreb, Department of Mathematics

    Professor Andrej Dujella

  24. A Pellian Equation with Primes and Applications to $$D(-1)$$ D ( ...

    Article • Bulletin of the Malaysian Mathematical Sciences Society, May 2018, Springer Science + Business Media

    Professor Andrej Dujella

  25. Elliptic curves induced by Diophantine triples

    Article • Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas, March 2018, Springer Science + Business Media

    Professor Andrej Dujella

  26. Triples which are D(n)-sets for several n's

    Article • Journal of Number Theory, March 2018, Elsevier

    Professor Andrej Dujella

  27. Absolute Real Root Separation

    Article • American Mathematical Monthly, January 2017, Mathematical Association of America

    Professor Andrej Dujella

  28. Root separation for reducible monic polynomials of odd degree

    Article • Rad Hrvatske akademije znanosti i umjetnosti Matematičke znanosti, January 2017, Croatian Academy of Sciences and Arts

    Professor Andrej Dujella

  29. More on Diophantine Sextuples

    Article • January 2017, Springer Science + Business Media

    Professor Andrej Dujella

  30. Elliptic curves with torsion group Z/6Z

    Article • Glasnik Matematicki, December 2016, University of Zagreb, Department of Mathematics

    Professor Andrej Dujella

  31. On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields

    Article • Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas, November 2016, Springer Science + Business Media

    Professor Andrej Dujella

  32. What is a Diophantine $m$-tuple?

    Article • Notices of the American Mathematical Society, August 2016, American Mathematical Society (AMS)

    Professor Andrej Dujella

  33. There Are Infinitely Many Rational Diophantine Sextuples

    Article • International Mathematics Research Notices, May 2016, Oxford University Press (OUP)

    Professor Andrej Dujella

  34. Finiteness results for F-Diophantine sets

    Article • Monatshefte für Mathematik, October 2015, Springer Science + Business Media

    Professor Andrej Dujella

  35. The rank and generators of Kihara’s elliptic curve with torsion $\mathbf{Z}/4\mathbf{Z}$ over $\mathbf{Q}(t)$

    Article • Proceedings of the Japan Academy Series A Mathematical Sciences, August 2015, Project Euclid

    Professor Andrej Dujella

  36. Elliptic Curves with Torsion Group ℤ/8ℤ or ℤ/2ℤ×ℤ/6ℤ

    Article • January 2015, American Mathematical Society (AMS)

    Professor Andrej Dujella

  37. The non-extensibility of $D(-2k+1)$-triples $\{1, k^2, k^2+2k-1\}$

    Article • Miskolc Mathematical Notes, January 2015, Mathematical Notes

    Professor Andrej Dujella

  38. On high rank $\pi/3$ and $2\pi/3$-congruent number elliptic curves

    Article • Rocky Mountain Journal of Mathematics, December 2014, Rocky Mountain Mathematics Consortium

    Professor Andrej Dujella

  39. Elliptic curves coming from Heron triangles

    Article • Rocky Mountain Journal of Mathematics, August 2014, Rocky Mountain Mathematics Consortium

    Professor Andrej Dujella

  40. Products of three factorial

    Article • Publicationes Mathematicae Debrecen, July 2014, University of Debrecen/ Debreceni Egyetem

    Professor Andrej Dujella

  41. Products of three factorials

    Article • Publicationes Mathematicae Debrecen, July 2014, University of Debrecen/ Debreceni Egyetem

    Professor Andrej Dujella

  42. On the torsion group of elliptic curves induced by D(4)-triples

    Article • Analele Universitatii Ovidius Constanta - Seria Matematica, June 2014, De Gruyter

    Professor Andrej Dujella

  43. High rank elliptic curves with prescribed torsion group over quadratic fields

    Article • Periodica Mathematica Hungarica, May 2014, Springer Science + Business Media

    Professor Andrej Dujella

  44. Some Diophantine properties of the sequence of S -units

    Article • Journal of Number Theory, May 2014, Elsevier

    Professor Andrej Dujella

  45. Root separation for reducible integer polynomials

    Article • Acta Arithmetica, January 2014, Institute of Mathematics, Polish Academy of Sciences

    Professor Andrej Dujella

  46. High-rank elliptic curves with torsion induced by Diophantine triples

    Article • LMS Journal of Computation and Mathematics, January 2014, Oxford University Press (OUP)

    Professor Andrej Dujella

  47. Diophantinem-tuples with elements in arithmetic progressions

    Article • Indagationes Mathematicae, January 2014, Elsevier

    Professor Andrej Dujella

  48. Arithmetic progressions and Pellian equations

    Article • Publicationes Mathematicae Debrecen, December 2013, University of Debrecen/ Debreceni Egyetem

    Professor Andrej Dujella

  49. Sumsets being squares

    Article • Acta Mathematica Hungarica, June 2013, Springer Science + Business Media

    Professor Andrej Dujella

  50. Elliptic curves and Triangles with three rational medians

    Article • Journal of Number Theory, June 2013, Elsevier

    Professor Andrej Dujella

  51. Ranks of Elliptic Curves with Prescribed Torsion over Number Fields

    Article • International Mathematics Research Notices, February 2013, Oxford University Press (OUP)

    Professor Andrej Dujella

  52. On the rank of elliptic curves coming from rational Diophantine triples

    Article • Rocky Mountain Journal of Mathematics, December 2012, Rocky Mountain Mathematics Consortium

    Professor Andrej Dujella

  53. Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization

    Article • Periodica Mathematica Hungarica, October 2012, Springer Science + Business Media

    Professor Andrej Dujella

  54. ON A VARIATION OF A CONGRUENCE OF SUBBARAO

    Article • Journal of the Australian Mathematical Society, October 2012, Cambridge University Press

    Professor Andrej Dujella

  55. On a problem of Diophantus for rationals

    Article • Journal of Number Theory, October 2012, Elsevier

    Professor Andrej Dujella

  56. On the sum of two divisors of (n 2 + 1)/2

    Article • Periodica Mathematica Hungarica, August 2012, Springer Science + Business Media

    Professor Andrej Dujella

  57. On power values of pyramidal numbers, I

    Article • Acta Arithmetica, January 2012, Institute of Mathematics, Polish Academy of Sciences

    Professor Andrej Dujella

  58. On a Conjecture Regarding Balancing with Powers of Fibonacci Numbers

    Article • Integers, January 2012, De Gruyter

    Professor Andrej Dujella

  59. On the size of sets whose elements have perfect power $n$-shifted products

    Article • Publicationes Mathematicae Debrecen, December 2011, University of Debrecen/ Debreceni Egyetem

    Professor Andrej Dujella

  60. Root separation for irreducible integer polynomials

    Article • Bulletin of the London Mathematical Society, October 2011, Oxford University Press (OUP)

    Professor Andrej Dujella

  61. Solving a family of quartic Thue inequalities using continued fractions

    Article • Rocky Mountain Journal of Mathematics, August 2011, Rocky Mountain Mathematics Consortium

    Professor Andrej Dujella

  62. On Hall's conjecture

    Article • Acta Arithmetica, January 2011, Institute of Mathematics, Polish Academy of Sciences

    Professor Andrej Dujella

  63. Root Separation for Reducible Monic Quartics

    Article • Rendiconti del Seminario Matematico della Università di Padova, January 2011, European Mathematical Publishing House

    Professor Andrej Dujella

  64. ON THE SIZE OF SETS IN A POLYNOMIAL VARIANT OF A PROBLEM OF DIOPHANTUS

    Article • International Journal of Number Theory, November 2010, World Scientific Pub Co Pte Lt

    Professor Andrej Dujella

  65. On the rank of elliptic curves over $\mathbf{Q}(i)$ with torsion group $\mathbf{Z}/4\mathbf{Z} \times \mathbf{Z}/4\mathbf{Z}$

    Article • Proceedings of the Japan Academy Series A Mathematical Sciences, June 2010, Project Euclid

    Professor Andrej Dujella

  66. A variant of Wiener’s attack on RSA

    Article • Computing, May 2009, Springer Science + Business Media

    Professor Andrej Dujella

  67. Rational Diophantine sextuples with mixed signs

    Article • Proceedings of the Japan Academy Series A Mathematical Sciences, April 2009, Project Euclid

    Professor Andrej Dujella

  68. A variant of Wiener's attack on RSA with small secret exponent

    Article • ACM Communications in Computer Algebra, July 2008, ACM (Association for Computing Machinery)

    Professor Andrej Dujella

  69. A POLYNOMIAL VARIANT OF A PROBLEM OF DIOPHANTUS FOR PURE POWERS

    Article • International Journal of Number Theory, February 2008, World Scientific Pub Co Pte Lt

    Professor Andrej Dujella

  70. Strong Diophantine Triples

    Article • Experimental Mathematics, January 2008, Taylor & Francis

    Professor Andrej Dujella

  71. Conjectures and results on the size and number of Diophantine tuples

    Article • January 2008, American Institute of Physics

    Professor Andrej Dujella

  72. On the number of Diophantine m-tuples

    Article • The Ramanujan Journal, December 2007, Springer Science + Business Media

    Professor Andrej Dujella

  73. On arithmetic progressions on Pellian equations

    Article • Acta Mathematica Hungarica, December 2007, Springer Science + Business Media

    Professor Andrej Dujella

  74. Decomposition of a recursive family of polynomials

    Article • Monatshefte für Mathematik, September 2007, Springer Science + Business Media

    Professor Andrej Dujella

  75. On Mordell-Weil groups of elliptic curves induced by Diophantine triples

    Article • Glasnik Matematicki, June 2007, University of Zagreb, Department of Mathematics

    Professor Andrej Dujella

  76. ON THE FAMILY OF DIOPHANTINE TRIPLES {k− 1,k+ 1, 16k3− 4k}

    Article • Glasgow Mathematical Journal, May 2007, Cambridge University Press

    Professor Andrej Dujella

  77. On Differences of Two Squares in Some Quadratic Fields

    Article • Rocky Mountain Journal of Mathematics, April 2007, Rocky Mountain Mathematics Consortium

    Professor Andrej Dujella

  78. On a Problem of Diophantus with Polynomials

    Article • Rocky Mountain Journal of Mathematics, February 2007, Rocky Mountain Mathematics Consortium

    Professor Andrej Dujella

  79. On the Indecomposability of Polynomials*

    Article • Sitzungsberichte und Anzeiger der mathematisch-naturwissenschaftlichen Klasse, January 2007, Osterreichische Akademie der Wissenschaften

    Professor Andrej Dujella

  80. Effective solution of the D(-1)-quadruple conjecture

    Article • Acta Arithmetica, January 2007, Institute of Mathematics, Polish Academy of Sciences

    Professor Andrej Dujella

  81. Diophantine m-tuples for linear polynomials II. Equal degrees

    Article • Journal of Number Theory, October 2006, Elsevier

    Professor Andrej Dujella

  82. INDECOMPOSABILITY OF POLYNOMIALS AND RELATED DIOPHANTINE EQUATIONS

    Article • The Quarterly Journal of Mathematics, November 2005, Oxford University Press (OUP)

    Professor Andrej Dujella

  83. COMPLETE SOLUTION OF A PROBLEM OF DIOPHANTUS AND EULER

    Article • Journal of the London Mathematical Society, February 2005, Oxford University Press (OUP)

    Professor Andrej Dujella

  84. Article • International Mathematics Research Notices, January 2005, Oxford University Press (OUP)

    Professor Andrej Dujella

  85. Bounds for the size of sets with the property D(n)

    Article • Glasnik Matematicki, December 2004, University of Zagreb, Department of Mathematics

    Professor Andrej Dujella

  86. Complete solution of the polynomial version of a problem of Diophantus

    Article • Journal of Number Theory, June 2004, Elsevier

    Professor Andrej Dujella

  87. There are only finitely many Diophantine quintuples

    Article • Journal für die reine und angewandte Mathematik (Crelles Journal), January 2004, De Gruyter

    Professor Andrej Dujella

  88. A family of quartic Thue inequalities

    Article • Acta Arithmetica, January 2004, Institute of Mathematics, Polish Academy of Sciences

    Professor Andrej Dujella

  89. A Polynomial Variant of a Problem of Diophantus and Euler

    Article • Rocky Mountain Journal of Mathematics, September 2003, Rocky Mountain Mathematics Consortium

    Professor Andrej Dujella

  90. On a problem of Diophantus for higher powers

    Article • Mathematical Proceedings of the Cambridge Philosophical Society, July 2003, Cambridge University Press

    Professor Andrej Dujella

  91. An example of elliptic curve over $\mathbf {Q}$ with rank equal to 15

    Article • Proceedings of the Japan Academy Series A Mathematical Sciences, September 2002, Project Euclid

    Professor Andrej Dujella

  92. A parametric family of quartic Thue equations

    Article • Acta Arithmetica, January 2002, Institute of Mathematics, Polish Academy of Sciences

    Professor Andrej Dujella

  93. On the size of Diophantine m-tuples

    Article • Mathematical Proceedings of the Cambridge Philosophical Society, January 2002, Cambridge University Press

    Professor Andrej Dujella

  94. An Absolute Bound for the Size of Diophantine m-Tuples

    Article • Journal of Number Theory, July 2001, Elsevier

    Professor Andrej Dujella

  95. Diophantine Equations for Second-Order Recursive Sequences of Polynomials

    Article • The Quarterly Journal of Mathematics, July 2001, Oxford University Press (OUP)

    Professor Andrej Dujella

  96. Diophantine $m$-tuples and elliptic curves

    Article • Journal de Théorie des Nombres de Bordeaux, January 2001, Cellule MathDoc/CEDRAM

    Professor Andrej Dujella

  97. Newton's Formula and the Continued Fraction Expansion of √d

    Article • Experimental Mathematics, January 2001, Taylor & Francis

    Professor Andrej Dujella

  98. Irregular Diophantine $m$-tuples and elliptic curves of high rank

    Article • Proceedings of the Japan Academy Series A Mathematical Sciences, May 2000, Project Euclid

    Professor Andrej Dujella

  99. Diophantine Triples and Construction of High-Rank Elliptic Curves over $bf Q$ with Three Non-Trivial 2-Torsion Points

    Article • Rocky Mountain Journal of Mathematics, March 2000, Rocky Mountain Mathematics Consortium

    Professor Andrej Dujella

  100. A parametric family of elliptic curves

    Article • Acta Arithmetica, January 2000, Institute of Mathematics, Polish Academy of Sciences

    Professor Andrej Dujella

  101. A bijective proof of Riordan's theorem on powers of Fibonacci numbers

    Article • Discrete Mathematics, March 1999, Elsevier

    Professor Andrej Dujella

  102. A Generalization of a Theorem of Baker and Davenport

    Article • The Quarterly Journal of Mathematics, September 1998, Oxford University Press (OUP)

    Professor Andrej Dujella

  103. A generalization of a theorem of Baker and Davenport

    Article • The Quarterly Journal of Mathematics, September 1998, Oxford University Press (OUP)

    Professor Andrej Dujella

  104. A Problem of Diophantus and Pell Numbers

    Article • January 1998, Springer Science + Business Media

    Professor Andrej Dujella

  105. On the Exceptional Set in the Problem of Diophantus and Davenport

    Article • January 1998, Springer Science + Business Media

    Professor Andrej Dujella

  106. On Diophantine quintuples

    Article • Acta Arithmetica, January 1997, Institute of Mathematics, Polish Academy of Sciences

    Professor Andrej Dujella

  107. Generalization of a problem of Diophantus

    Article • Acta Arithmetica, January 1993, Institute of Mathematics, Polish Academy of Sciences

    Professor Andrej Dujella

  108. A note on Diophantine quintuples

    Article • De Gruyter

    Professor Andrej Dujella

  109. A problem of Diophantus and Dickson's conjecture

    Article • De Gruyter

    Professor Andrej Dujella