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ArticleOriginal scientific text

Title

On Diophantine quintuples

Authors 1

Affiliations

  1. Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia

Bibliography

  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).
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  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).
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  12. P. Heichelheim, The study of positive integers (a,b) such that ab + 1 is a square, Fibonacci Quart. 17 (1979), 269-274.
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  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.
Acta Arithmetica
1997/81/1
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Pages:
69-79
Main language of publication
English
Received
1996-10-08
Published
1997
Exact and natural sciences