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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.

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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.

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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. Petho, 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. Petho 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. Petho, 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 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. Petho, 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 P_t 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 (x^k-1)(y^k-1) = (z^k-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.

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

130. R. Dietmann, C. Elsholtz, K. Gyarmati and 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, Int. Math. Res. Not. 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, 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 and H. Senay, Constructions of some new nonextandable P_k 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, preprint.

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 {F_2k+1, F_2k+3, F_2k+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), 15-29.

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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 P_k 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.

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184. F. Najman, Compact representation of quadratic integers and integer points on some elliptic curves, Rocky Mountain J. Math. 40 (2010), 1979-2002.

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520. A. Dujella, M. Kazalicki, V. Petricevic, Rational Diophantine sextuples with strong pair, preprint, 2024.

521. S. Kim, C. H. Yip, S. Yoo, Explicit constructions of Diophantine tuples over finite fields, Ramanujan J. 65 (2024), 163-172.

522. M. Cipu, Y. Fujita, M. Mignotte, Diophantine triples with three parameters, Res. Number Theory 10 (2024), Article number 44.

523. E. Barbeau, Gregarious and reclusive triples. Part A: A visit to the land of Fibonacci, Crux Mathematicorum 50 (2024), 190-192.

524. M. Jukic Bokun, I. Soldo, Extensions of D(−1)-pairs in some imaginary quadratic fields, New York J. Math. 30 (2024), 745-755.

525. N. Irmak, On k-generalized Fibonacci Diophantine triples, Math. Commun. 29 (2024), 203-216.

526. K. Brown, Numbers, 2023, Sections 1.7, 1.9, 1.12, 1.13, 3.2, 3.11, 14.5.

527. S. Kim, C. H. Yip, S. Yoo, Paley-like quasi-random graphs arising from polynomials, preprint, 2024.

528. C. H. Yip, S. Yoo, F-Diophantine sets over finite fields, preprint, 2024.

529. C. H. Yip, Improved upper bounds on Diophantine tuples with the property D(n), Bull. Aust. Math. Soc., to appear.

530. A. Dujella, Diophantine m-tuples and Elliptic Curves, Springer, Cham, 2024.

531. E. Barbeau, Gregarious and reclusive triples. Part B: A plethora of triples and quadruples, Crux Mathematicorum 50 (2024), 244-247.

532. C. H. Yip, Topics in arithmetic combinatorics, PhD Thesis, University of British Columbia, 2024.

533. E. Barbeau, Gregarious and reclusive triples. Part C: Finding triples when some elements are known, Crux Mathematicorum 50 (2024), 290-293.

534. R. Rathbun, 2001 Diophantine sextuples of low height, Zenodo, 2024, https://doi.org/10.5281/zenodo.13362704

535. T. Yesin Elsheikh, Divisibility of Rational Points on Elliptic Curves and Arithmetic Progressions in Polynomial Dynamical Systems, PhD thesis, Sabanci University, Istanbul, 2023.

536. R. Rathbun, The search for Diophantine sextuples and a possible septuple, distributed computing project, 2024, http://www.numbertheory.org/ntw/pdfs/search_for_Diophantine_sextuples.pdf

537. A. Dujella, Triples, quadruples and quintuples which are D(n)-sets for several n's, in: Class Groups of Number Fields and Related Topics (K. Chakraborty, A. Hoque and P. P. Pandey, Eds.), Springer, Cham, 2024, to appear.

538. G. McShane, Diophantine triples and Ptolemy relation, preprint, 2024.

539. N. Irmak, On k-generalized Fibonacci Diophantine triples, Math. Commun. 29 (2024), 203-216.

540. J. Badesa, On the asymptotics of D(n)-pairs and triples, preprint, 2024.

541. J. M. Mouanda, K. K. Vincent, On matrix strong Diophantine 27-tuples and matrix elliptic curves, Mathematics and Systems Science 2(2) (2024), Article ID: 2624.

542. G. Batta, L. Hajdu, A. Pongracz, On Diophantine graphs, preprint, 2024.

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