On Diophantine quintuples

• Autorzy: Andrej Dujella
• Języki publikacji: EN

Kategorie tematyczne

• 11D99: None of the above, but in this section
• 11D09: Quadratic and bilinear equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 81
• Numer: 1
• Strony: 69-79

Daty

wydano

1997

otrzymano

1996-10-08

Twórcy

autor

Andrej Dujella

• Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia

Bibliografia

• [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.
• [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.
• [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.
• [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] Diophantus of Alexandria, Arithmetics and the Book of Polygonal Numbers, Nauka, Moscow, 1974 (in Russian).
• [6] A. Dujella, Generalization of a problem of Diophantus, Acta Arith. 65 (1993), 15-27.
• [7] A. Dujella, Diophantine quadruples for squares of Fibonacci and Lucas numbers, Portugal. Math. 52 (1995), 305-318.
• [8] A. Dujella, Generalized Fibonacci numbers and the problem of Diophantus, Fibonacci Quart. 34 (1996), 164-175.
• [9] A. Dujella, Generalization of the Problem of Diophantus and Davenport, Dissertation, University of Zagreb, 1996 (in Croatian).
• [10] A. Dujella, Some polynomial formulas for Diophantine quadruples, Grazer Math. Ber. 328 (1996), 25-30.
• [11] A. Dujella, A problem of Diophantus and Pell numbers, in: Application of Fibonacci Numbers, Vol. 7, Kluwer, Dordrecht, to appear.
• [12] P. Heichelheim, The study of positive integers (a,b) such that ab + 1 is a square, Fibonacci Quart. 17 (1979), 269-274.
• [13] V. E. Hoggatt and G. E. Bergum, A problem of Fermat and the Fibonacci sequence, ibid. 15 (1977), 323-330.
• [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] 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.
• [16] V. K. Mootha, On the set of numbers {14,22,30,42,90}, Acta Arith. 71 (1995), 259-263.
• [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.