Diophantine m-tuples references (chronologically):

  1. M. Gardner, Mathematical diversions, Scientific American 216 (1967), March 1967, p. 124; April 1967, p.119.

  2. J. H. van Lint, On a set of diophantine equations, T. H.-Report 68 - WSK-03, Department of Mathematics, Technological University Eindhoven, Eindhoven, 1968.

  3. A. Baker and H. Davenport, The equations 3x2 - 2 = y2 and 8x2 - 7 = z2, Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137.

  4. P. Kanagasabapathy and T. Ponnudurai, The simultaneous Diophantine equations y2 - 3x2 = -2 and z2 - 8x2 = -7, Quart. J. Math. Oxford Ser. (2) 26 (1975), 275-278.

  5. B. W. Jones, A variation on a problem of Davenport and Diophantus, Quart. J. Math. Oxford Ser. (2) 27 (1976), 349-353.

  6. G. Sansone, Il sistema diofanteo N + 1 = x2, 3N + 1 = y2, 8N + 1 = z2, Ann. Mat. Pura Appl. (4) 111 (1976), 125-151.

  7. M. Gardner, Mathematical Magic Show, Alfred Knopf, New York, 1977, pp. 210, 221-222.

  8. V. E. Hoggatt and G. E. Bergum, A problem of Fermat and the Fibonacci sequence, Fibonacci Quart. 15 (1977), 323-330.

  9. G. Berzsenyi, Problem B-369, Fibonacci Quart. 16 (1978), 565.

  10. P. E. Gibbs, Computer Bulletin 17 (1978), 16.

  11. C. M. Grinstead, On a method of solving a class of Diophantine equations, Math. Comp. 32 (1978), 936-940.

  12. B. W. Jones, A second variation on a problem of Diophantus and Davenport, Fibonacci Quart. 16 (1978), 155-165.

  13. C. Leach, Computer Bulletin 15 (1978), 13.

  14. J. Arkin, V. E. Hoggatt and E. G. Strauss, On Euler's solution of a problem of Diophantus, Fibonacci Quart. 17 (1979), 333-339.

  15. P. Heichelheim, The study of positive integers (a,b) such that ab + 1 is a square, Fibonacci Quart. 17 (1979), 269-274.

  16. J. Arkin, V. E. Hoggatt and E. G. Strauss, On Euler's solution of a problem of Diophantus II, Fibonacci Quart. 18 (1980), 170-176.

  17. N. Thamotherampillai, The set of numbers {1,2,7}, Bull. Calcutta Math. Soc. 72 (1980), 195-197.

  18. M. Veluppillai, The equations z2 - 3y2 = -2 and z2 - 6x2 = -5, A Collection of Manuscripts Related to the Fibonacci sequence, (V. E. Hoggatt, M. Bicknell-Johnson, eds.), The Fibonacci Association, Santa Clara}, 1980, pp. 71-75.

  19. J. Morgado, Generalization of a result of Hoggatt and Bergum on Fibonacci numbers, Portugaliae Math. 42 (1983-1984), 441-445.

  20. S. P. Mohanty and A. M. S. Ramasamy, The simultaneous Diophantine equations 5y2 - 20 = x2 and 2y2 + 1 = z2, J. Number Theory 18 (1984), 356-359.

  21. E. Brown, Sets in which xy + k is always a square, Math. Comp. 45 (1985), 613-620.

  22. H. Gupta and K. Singh, On k-triad sequences, Internat. J. Math. Math. Sci. 5 (1985), 799-804.

  23. S. P. Mohanty and A. M. S. Ramasamy, The characteristic number of two simultaneous Pell's equations and its application, Simon Stevin 59 (1985), 203-214.

  24. S. P. Mohanty and A. M. S. Ramasamy, On Pr,k sequences, Fibonacci Quart. 23 (1985), 36-44.

  25. M. Nutt, Generalizations of Thamotherampillai's {1,2,7}, Bull. Calcuta Math. Soc. 78 (1986), 7-9.

  26. A. F. Horadam, Generalization of a result of Morgado, Portugaliae Math. 44 (1987), 131-136.

  27. J. Morgado, A problem concerning the Fibonacci numbers, Proceedings of the Second Meeting of Portuguese Algebraist, Univ. Porto, Porto, 1987, pp. 77-88 (in Portuguese).

  28. D. X. Zheng, On the system of Diophantine equations y2 - 2x2 = 1, z2 - 5x2 = 4 and y2 - 5x2 = 4, z2 - 10x2 = 9, Sichuan Daxue Xuebao 24 (1987), 25-29 (in Chinese).

  29. J. Arkin and G. E. Bergum, More on the problem of Diophantus, Application of Fibonacci Numbers, Vol. 2 (A. N. Philippou, A. F. Horadam, G. E. Bergum, eds.), Kluwer, Dordrecht, 1988, pp. 177-181.

  30. G. Berzsenyi, Problems, puzzles, paradoxes, Consortium 25 (1988), 5.

  31. C. Long and G. E. Bergum, On a problem of Diophantus, Application of Fibonacci Numbers, Vol 2 (A. N. Philippou, A. F. Horadam, G. E. Bergum, eds.), Kluwer, Dordrecht, 1988, pp. 183-191.

  32. A. G. Shannon, Fibonacci numbers and Diophantine quadruples: Generalizations of results of Morgado and Horadam, Portugaliae Math. 45 (1988), 165-169.

  33. V. K. Mootha and G. Berzsenyi, Characterization and extendibility of Pt-sets, Fibonacci Quart. 27 (1989), 287-288.

  34. H. Altindis, Generalization of the set {1,2,5}, Istanbul Univ. Fen Fak. Mat. Derg. 49 (1990), 1-5.

  35. J. H. Chen, Common solutions of the Pell equations x2 - 2y2 = 1 and y2 - Dz2 = 4, J. Wuhan Univ. Natur. Sci. Ed. (1990), 8--12.

  36. A. Dujella, A problem of Diophantus and Fibonacci numbers, Matematika (Zagreb) 19 (3) (1990), 45-52 (in Croatian).

  37. D. Zagier, Elliptische Kurven: Fortschritte und Anwendungen, Jahresber. Deutsch. Math.-Verein 92 (1990), 58-76.

  38. G. Berzsenyi, Adventures among Pt-sets, Quantum 1 (4) (1991), 57.

  39. J. Morgado, Note on a Shannon's theorem concerning the Fibonacci numbers and Diophantine quadruples, Portugaliae Math. 48 (1991), 429-439.

  40. D. M. Bloom, Problem 10238, Amer. Math. Monthly 99 (1992), 674.

  41. J. Roberts, Lure of the Integers, The Mathematical Association of America, 1992, pp. 31-35.

  42. D. X. Zheng, On the system of Diophantine equations a2x2 - a1y2 = a2 - a1, a3y2 - a2z2 = a3 - a2, Sichuan Daxue Xuebao 29 (1992), 348-351 (in Chinese).

  43. J. Arkin, D. C. Arney, F. R. Giordano, R. A. Kolb and G. E. Bergum, An extension of an old classical Diophantine problem, Application of Fibonacci Numbers, Vol. 5 (G. E. Bergum, A. N. Philippou, A. F. Horadam, eds.), Kluwer, Dordrecht, 1993, pp. 45-48.

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

  45. H. Altindis, On P2j2 sets, Bull. Calcuta Math. Soc. 86 (1994), 305-306.

  46. G. Berzsenyi, Problem 4/14, Mathematics and Informatics Quarterly 5 (1995), 103-105.

  47. R. Drnovsek, Solution of Problem 10238, Amer. Math. Monthly 102 (1995), 275-276.

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

  49. V. K. Mootha, On the set of numbers {14,22,30,42,90}, Acta Arith. 71 (1995), 259-263.

  50. J. Morgado, Note on the Chebyshev polynomials and applications to the Fibonacci numbers, Portugaliae Math. 52 (1995), 363-378.

  51. A. M. S. Ramasamy, A remarkable sequence, Banyan Mathematical Journal 2 (1995), 69-76.

  52. Gh. Udrea, A problem of Diophantos-Fermat and Chebyshev polynomials of the second kind, Portugaliae Math. 52 (1995), 301-304.

  53. Z. Y. Chen, The Diophantine system of equations 5x2 - 3y2 = 2, 16y2 - 5z2 = 11, J. Central China Normal Univ. Natur. Sci. 30 (1996), 381-384 (in Chinese).

  54. M. N. Deshpande and G. E. Bergum, Interesting arrays associated with Fibonacci sequences, Applications of Fibonacci Numbers, Vol. 6 (G. E. Bergum, A. N. Philippou, A. F. Horadam, eds.), Kluwer, Dordrecht, 1996, pp. 85-92.

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

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

  57. A. Dujella, Generalization of the Problem of Diophantus and Davenport, Dissertation, University of Zagreb, 1996 (in Croatian).

  58. S. T. Thakar, The role of "T" and "S" of IMTS, Mathematics and Informatics Quarterly 6 (1996), 23-26.

  59. Gh. Udrea, A note on the sequence (Wn) of A. F. Horadam, Portugaliae Math. 53 (1996), 143-155.

  60. Z. Y. Chen, Upper bounds for positive integer solutions of the indeterminate equations x2 - 7y2 = 2, z2 - 32y2 = -23, J. Central China Normal Univ. Natur. Sci. 31 (1997), 253-256 (in Chinese).

  61. M. N. Deshpande, Problem 10622, Amer. Math. Monthly 104 (1997), 870.

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

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

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

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

  66. M. N. Deshpande, One property of triangular numbers, Portugaliae Math. 55 (1998), 381-383.

  67. 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.

  68. 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.

  69. 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.

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

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

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

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

  74. K. S. Kedlaya, When is (xy+1)(yz+1)(zx+1) a square?, Math. Mag. 71 (1998), 61-63.

  75. K. S. Kedlaya, Solving constrained Pell equations, Math. Comp. 67 (1998), 833-842.

  76. Z. Y. Chen, The system of Diophantine equations (m + 2)x2 - my2 = 2, (4m + 4)y2 - (m + 2)z2 = 3m + 2, J. Central China Normal Univ. Natur. Sci. 33 (1999), 1-5.

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

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

  79. Z. Franco, Solution of Problem 10622, Amer. Math. Monthly 106 (1999), 868.

  80. P. Gibbs, A generalised Stern-Brocot tree from regular Diophantine quadruples, XXX Mathematics Archive math.NT/9903035.

  81. E. Herrmann, A. Pethoe and H. G. Zimmer, On Fermat's quadruple equations, Abh. Math. Sem. Univ. Hamburg 69 (1999), 283-291.

  82. L. Jones, A polynomial approach to a Diophantine problem, Math. Mag. 72 (1999), 52-55.

  83. A. Pethoe, Algebraische Algorithmen, Vieweg, Braunschweig, 1999, pp. 106-115.

  84. E. W. Weisstein, CRC Concise Encyclopedia of Mathematics, Chapman & Hall / CRC, Boca Raton, 1999, p. 759.

  85. H. Widmer, Solution of Problem 10622, Amer. Math. Monthly 106 (1999), 867-868.

  86. M. N. Deshpande, An interesting conjecture, The Mathematical Gazette 84 (2000), 296-298.

  87. 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.

  88. 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.

  89. A. Dujella, A parametric family of elliptic curves, Acta Arith. 94 (2000), 87-101.

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

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

  92. O. Kihel, On the extendibility of the P-1-set {1,2,5}, Fibonacci Quart. 38 (2000), 464-466.

  93. Gh. Udrea, A problem of Diophantus-Fermat and Chebyshev polynomials of the first kind, Rev. Roumaine Math. Pures Appl. 45 (2000), 531-535.

  94. E. Assaf and S. Gueron, Characterization of regular Diophantine quadruples, Elem. Math. 56 (2001), 71-81.

  95. M. N. Deshpande and E. Brown, Diophantine triplets and the Pell sequence, Fibonacci Quart. 39 (2001), 242-249.

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

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

  98. P. Gibbs, Diophantine quadruples and Cayley's hyperdeterminant, XXX Mathematics Archive math.NT/0107203

  99. K. Gyarmati, On a problem of Diophantus, Acta Arith. 97 (2001), 53-65.

  100. K. Gyarmati, Powers, powerful and powerfree numbers in sumsets and multiplicative structures, Master Thesis, Eotvos University, Budapest, 2001 (in Hungarian).

  101. A. Kihel and O. Kihel, Sets in which the product of any k elements increased by t is a kth-power, Fibonacci Quart. 39 (2001), 98-100.

  102. A. Kihel and O. Kihel, On the intersection and the extendability of Pt sets, Far East J. Math. Sci. 3 (2001), 637-643.

  103. A. F. Beardon and M. N. Deshpande, Diophantine triples, The Mathematical Gazette 86 (2002), 258-260.

  104. M. N. Deshpande, One interesting family of diophantine triplets, Internat. J. Math. Ed. Sci. Tech. 33 (2002), 253-256.

  105. M. N. Deshpande, A problem in number theory, Resonance 7(7) (2002), 89-91.

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

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

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

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

  110. C. Fuchs, Quantitative finiteness results for Diophantine equations, Dissertation, TU Graz, 2002.

  111. K. Gyarmati, A. Sarkozy and C. L. Stewart, On shifted products which are powers, Mathematika 49 (2002), 227-230.

  112. M. J. Jacobson, Jr. and H. C. Williams, Modular arithmetic on elements of small norm in quadratic fields, Des. Codes and Cryptogr. 27 (2002), 93-110.

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

  114. M. N. Deshpande, Families of Diophantine triplets, Bulletin of the Marathwada Mathematical Society, 4 (2003), 19-21.

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

  116. F. S. Abu Muriefah and A. Al- Rashed, On the exendibility of the Diophantine triple {1,5,c}, Internat. J. Math. Math. Sci. 33 (2004), 1737-1746.

  117. F. S. Abu Muriefah and A. Al- Rashed, Some Diophantine quadruples in the ring Z[√-2], Math. Commun. 9 (2004), 1-8.

  118. J. Almeida and A. Machiavelo, Jose Morgado, Bulletin of International Center for Mathematics 17 (2004), 24-27.

  119. J. Almeida and A. Machiavelo, Jose Morgado: in memoriam, Boletim da SPM 50 (2004), 1-18.

  120. Y. Bugeaud, On the Diophantine equation (xk-1)(yk-1) = (zk-1), Indag. Math. 15 (2004), 21-28.

  121. Y. Bugeaud and K. Gyarmati, On generalizations of a problem of Diophantus, Illinois J. Math. 48 (2004), 1105-1115.

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

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

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

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

  126. Z. Franusic, Diophantine quadruples in the ring Z[√2], Math. Commun. 9 (2004), 141-148.

  127. R. K. Guy, Unsolved Problems in Number Theory, 3rd edition, Springer-Verlag, New York, 2004, Section D29, p. 310.

  128. D. Saraswathy, A Study on Sets of Numbers with Diophantine Property, M.Phil. Dissertation, Department of Mathematics, Pondicherry University, Pondicherry, 2004.

  129. M. Waldschmidt, Open Diophantine problems, Moscow Math. J. 4 (2004), 245-305.

  130. R. Dietmann, C. Elsholtz, K. Gyarmati, M. Simonovits, Shifted products that are coprime pure powers, J. Combin. Theory Ser. A 111 (2005), 24-36.

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

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

  133. 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.

  134. A. Filipin, Non-extendibility of D(-1)-triples of the form {1,10,c}, Internat. J. Math. Math. Sci. 35 (2005) 2217-2226.

  135. Z. Franusic, Diophantine Quadruples in Quadratic Fields, Dissertation, University of Zagreb, 2005 (in Croatian).

  136. C. Fuchs, Upper Bounds for the Solutions of Diophantine Problems, Habilitation Thesis, TU Graz, 2005.

  137. K. Gyarmati, A polynomial extension of a problem of Diophantus, Publ. Math. Debrecen 66 (2005), 389-405.

  138. F. Luca, On shifted products which are powers, Glas. Mat. Ser. III 40 (2005), 13-20.

  139. F. S. Abu Muriefah and A. Al- Rashed, On the simultaneous Diophantine equations y2 - 5x2 = 4 and z2 - 442x2 = 441, Arab. J. Sci. Eng. Sect. A Sci. 31 (2006) 207-211.

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

  141. A. Filipin, Systems of Pellian Equations and the Problem of Extension of Some Diophantine Triples, Dissertation, University of Zagreb, 2006 (in Croatian).

  142. Y. Fujita, The unique representation d = 4k(k2 - 1) in D(4)-quadruples {k-2, k+2, 4k, d}, Math. Commun. 11 (2006), 69-81.

  143. Y. Fujita, The non-extensibility of D(4k)-triples {1, 4k(k-1), 4k2+1} with |k| prime, Glas. Mat. Ser. III, 41 (2006), 205-216.

  144. P. Gibbs, Some rational Diophantine sextuples, Glas. Mat. Ser. III 41 (2006), 195-203.

  145. P.-C. Hu, C.-C. Yang, Value Distribution Theory Related to Number Theory, Birkhäuser, Basel, 2006, pp. 335-336.

  146. Y. Li, An upper bound for the positive integer solutions of the system of Diophantine equations 7x2-5y2=2, 24y2-7z2=17, J. Chongqing Norm. Univ. Nat. Sci. Ed. 23 (2006), 33-35. (in Chinese).

  147. A. Silvester, Fast and Unconditional Principal Ideal Testing, Master's thesis, University of Calgary, 2006.

  148. Y. Bugeaud, A. Dujella and M. Mignotte, On the family of Diophantine triples {k - 1, k + 1, 16k^3 - 4k}, Glasgow Math. J. 49 (2007), 333-344.

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

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

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

  152. A. Filipin, Extensions of some parametric families of D(16)-triples, Internat. J. Math. Math. Sci. 2007 (2007), Article ID 63739, 12 pages

  153. Y. Fujita, The extensibility of D(-1)-triples {1,b,c}, Publ. Math. Debrecen 70 (2007), 103-117.

  154. Y. Fujita, The D(1)-extensions of D(-1)-triples {1, 2, c} and integer points on the attached elliptic curves, Acta Arith. 128 (2007), 349-375.

  155. K. Gyarmati and C. L. Stewart, On powers in shifted products, Glas. Mat. Ser. III 42 (2007), 273-279.

  156. T. Liqun, On the property P-1, Integers 7 (2007), #A47

  157. K. Kaygisiz, H. Senay, Constructions of some new nonextandable Pk sets, International Mathematical Forum 2 (2007), 2869-2874.

  158. A. M. S. Ramasamy, Sets and sequences linked with a question of Diophantus, Bulletin of Kerala Mathematics Association 4 (2007), 109-125.

  159. M. N. Deshpande, Diophantine triples from recurrence relations, Internat. J. Math. Ed. Sci. Tech., to appear.

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

  161. 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.

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

  163. A. Filipin, On the size of sets in which xy + 4 is always a square, Rocky Mountain J. Math. 39 (2009), 1195-1224.

  164. A. Filipin, There does not exist a D(4)-sextuple, J. Number Theory 128 (2008), 1555-1565.

  165. A. Filipin and Y. Fujita, Any polynomial D(4)-quadruple is regular, Math. Commun. 13 (2008), 45-55.

  166. Z. Franusic, Diophantine quadruples in Z[√(4k+3)], Ramanujan J. 17 (2008), 77-88.

  167. Z. Franusic, A Diophantine problem in Z[(1+√d)/2], Studia Sci. Math. Hungar. 46 (2009), 103-112.

  168. Y. Fujita, The extensibility of Diophantine pairs {k-1, k+1}, J. Number Theory 128 (2008), 322-353.

  169. Y. Fujita, The Hoggatt-Bergum conjecture on D(-1)-triples {F2k+1, F2k+3, F2k+5} and integer points on the attached elliptic curves, Rocky Mountain J. Math. 39 (2009), 1907-1932.

  170. C. L. Stewart, On sets of integers whose shifted products are powers, J. Combin. Theory Ser. A 115 (2008), 662-673.

  171. G. Campbell and E. H. Goins, Heron triangles, Diophantine problems and elliptic curves, preprint.

  172. Y. Fujita, Any Diophantine quintuple contains a regular Diophantine quadruple, J. Number Theory 129 (2009), 1678-1697.

  173. Y. Fujita, The number of Diophantine quintuples, Glas. Mat. Ser. III 45 (2010), to appear.

  174. A. J. MacLeod, Square Eulerian quadruples, XXX Mathematics Archive math.NT/0609127, preprint.

  175. D. S. Nagaraj and P. Shastri, On the determination of Diophantine triples, in: Number Theory and Applications (S. D. Adhikari, B. Ramakrishnan, eds.), Hindustan Book Agency, 2009, pp. 139-148.

  176. R. Tamura, Non-extendibility of D(-1)-triples {1,b,c}, preprint.

  177. C. Fuchs, F. Luca and L. Szalay, Diophantine triples with values in binary recurrences, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 7 (2008), 579-608.

  178. F. Luca and L. Szalay, Fibonacci Diophantine triples, Glas. Mat. Ser. III 43 (2008), 253-264.

  179. K. Kaygisiz, H. Senay and N. Bircan, Construction of some new nonextended Pk sets, preprint.

  180. 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.

  181. Y. Fujita, Diophantine quadruples containing some triples and the number of Diophantine quintuples, Diophantine Analysis and Related Fields (DARF 2007/2008), AIP Conf. Proc. 976 (T. Komatsu, ed.), Amer. Inst. Phys., Melville, NY, 2008, pp. 90-95.

  182. Z. Franusic, On the extensibility of Diophantine triples {k-1, k+1, 4k} for Gaussian integers, Glas. Mat. Ser. III 43 (2008), 265-291.

  183. J.-M. de Koninck, A. Mercier, 1001 Problems in Classical Number Theory, American Mathematical Society, Providence, 2007, pp. 284-285.

  184. F. Najman, Compact representation of quadratic integers and integer points on some elliptic curves, Rocky Mountain J. Math., to appear.

  185. A. Filipin, An irregular D(4)-quadruple cannot be extended to a quintuple, Acta Arith. 136 (2009), 167-176.

  186. F. Najman, Integer points on two families of elliptic curves, Publ. Math. Debrecen, to appear.

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

  188. Bo He, A. Togbe, On the family of Diophantine triples {k+1, 4k, 9k+3}, Period. Math. Hungar. 58 (2009), 59-70.

  189. Bo He, A. Togbe, On a family of Diophantine triples {k, A2k+2A, (A+1)2k+2(A+1)} with two parameters, Acta Math. Hungar. 124 (2009), 99-113.

  190. A. Filipin, There are only finitely many D(4)-quintuples, Rocky Mountain J. Math., to appear.

  191. A. Filipin, A. Togbe, On the family of Diophantine triples {k+2, 4k, 9k+6}, Acta Math. Acad. Paedagog. Nyhazi. 25 (2009), 145-153.

  192. F. Luca and L. Szalay, Lucas Diophantine triples, Integers 9 (2009), #A35, 441-457.

  193. S.-C. Yang, On the solutions of the Pell Equations x2-7y2=2, 32y2-z2=23, Journal of Tianzhong 22 (2007). (in Chinese).

  194. W. D. Banks, F. Luca and L. Szalay, A variant on the notion of a diophantine s-tuple, Glasgow Math. J. 51 (2009), 83-89.

  195. G. Martin and S. Sitar, Erdös-Turán with a moving target, equidistribution of roots of reducible quadratics, and Diophantine quadruples, preprint.

  196. 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.

  197. H. Balasunderam, The set of numbers {1, 5, 10}, J. Natn. Sci. Coun. Sri Lanka 6 (1978), 23-26.

  198. P. Gibbs, Adjugates of Diophantine Quadruples, preprint, viXra:0907.0024

  199. A. Dujella and I. Soldo, Diophantine quadruples in Z[√-2], An. Stiint. Univ. "Ovidius" Constanta Ser. Mat., to appear.

  200. J.-M. de Koninck, Those Fascinating Numbers, American Mathematical Society, Providence, 2009, p. 120.

  201. A. Filipin, On the polynomial parametric family of the sets with the property D(-1;1), Bol. Soc. Mat. Mexicana, to appear.

  202. Y. Fujita, Extensions of the D(∓k2)-triples {k2, k2 ± 1, 4k2 ± 1}, Period. Math. Hungar. 59 (2009), 21-33.

  203. A. Filipin, B. He, A. Togbe, On a family of two-parametric D(4)-triples, preprint.

  204. A. Filipin, B. He, A. Togbe, On the D(4)-triple { F2k, F2k+6, 4F2k+4 }, Fibonacci Quart., to appear.

  205. A. Filipin, Y. Fujita, The number of D(-1)-quadruples, preprint.

  206. H. Hemme, Mathematik zum Frühstück. 89 mathematische Rätsel mit ausführlichen Lösungen, Vandenhoeck & Ruprecht, Göttingen, 1990, p. 40, 130.

  207. B. Sriraman, H. Adrian, The existential void in learning: Juxtaposing mathematics and literature, in: Interdisciplinarity, Creativity, and Learning (B. Sriraman, V. Freiman, N. Lirette-Pitre, eds.), Age Publishing, 2009, pp. 13-29.

Classical references (Diophantus, Fermat, Euler)

Links to related sites

Papers of Andrej Dujella

1. Introduction
2. Diophantine quintuple conjecture
3. Sets with the property D(n)
4. Connections with Fibonacci numbers
5. Rational Diophantine m-tuples
6. Connections with elliptic curves
7. Various generalizations

Diophantine m-tuples page Andrej Dujella home page