On Diophantine quintuples

 Access to full text

 Full (PDF)

1. [1] J. Arkin, D. C. Arney, F. R. Giordano, R. A. Kolb and G. E. Bergum, An extension of an old classical Diophantine problem, in: Application of Fibonacci Numbers, Vol. 5, G. E. Bergum, A. N. Philippou and A. F. Horadam (eds.), Kluwer, Dordrecht, 1993, 45-48. Zbl0891.11007
2. [2] J. Arkin and G. E. Bergum, More on the problem of Diophantus, in: Application of Fibonacci Numbers, Vol. 2, A. N. Philippou, A. F. Horadam and G. E. Bergum (eds.), Kluwer, Dordrecht, 1988, 177-181. Zbl0649.10011
3. [3] J. Arkin, V. E. Hoggatt and E. G. Straus, On Euler's solution of a problem of Diophantus, Fibonacci Quart. 17 (1979), 333-339. Zbl0418.10021
4. [4] H. Davenport and A. Baker, The equations 3x²-2 = y² and 8x²-7 = z², Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137. 
5. [5] Diophantus of Alexandria, Arithmetics and the Book of Polygonal Numbers, Nauka, Moscow, 1974 (in Russian). 
6. [6] A. Dujella, Generalization of a problem of Diophantus, Acta Arith. 65 (1993), 15-27. Zbl0849.11018
7. [7] A. Dujella, Diophantine quadruples for squares of Fibonacci and Lucas numbers, Portugal. Math. 52 (1995), 305-318. Zbl0844.11015
8. [8] A. Dujella, Generalized Fibonacci numbers and the problem of Diophantus, Fibonacci Quart. 34 (1996), 164-175. Zbl0856.11017
9. [9] A. Dujella, Generalization of the Problem of Diophantus and Davenport, Dissertation, University of Zagreb, 1996 (in Croatian). 
10. [10] A. Dujella, Some polynomial formulas for Diophantine quadruples, Grazer Math. Ber. 328 (1996), 25-30. Zbl0882.11018
11. [11] A. Dujella, A problem of Diophantus and Pell numbers, in: Application of Fibonacci Numbers, Vol. 7, Kluwer, Dordrecht, to appear. Zbl0920.11011
12. [12] P. Heichelheim, The study of positive integers (a,b) such that ab + 1 is a square, Fibonacci Quart. 17 (1979), 269-274. Zbl0416.10011
13. [13] V. E. Hoggatt and G. E. Bergum, A problem of Fermat and the Fibonacci sequence, ibid. 15 (1977), 323-330. Zbl0383.10007
14. [14] C. Long and G. E. Bergum, On a problem of Diophantus, in: Application of Fibonacci Numbers, Vol. 2, A. N. Philippou, A. F. Horadam and G. E. Bergum (eds.), Kluwer, Dordrecht, 1988, 183-191. 
15. [15] S. P. Mohanty and M. S. Ramasamy, The characteristic number of two simultaneous Pell's equations and its application, Simon Stevin 59 (1985), 203-214. Zbl0575.10010
16. [16] V. K. Mootha, On the set of numbers {14,22,30,42,90}, Acta Arith. 71 (1995), 259-263. Zbl0820.11014
17. [17] M. Veluppillai, The equations z²-3y² = -2 and z²-6x² = -5, in: A Collection of Manuscripts Related to the Fibonacci Sequence, V. E. Hoggatt and M. Bicknell-Johnson (eds.), The Fibonacci Association, Santa Clara, 1980, 71-75. 

1. Andrej Dujella, Diophantine $m$-tuples and elliptic curves