# Generalization of a problem of Diophantus

Acta Arithmetica (1993)

- Volume: 65, Issue: 1, page 15-27
- ISSN: 0065-1036

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topAndrej Dujella. "Generalization of a problem of Diophantus." Acta Arithmetica 65.1 (1993): 15-27. <http://eudml.org/doc/206559>.

@article{AndrejDujella1993,

author = {Andrej Dujella},

journal = {Acta Arithmetica},

keywords = {perfect squares; Fibonacci numbers; property of Diophantus},

language = {eng},

number = {1},

pages = {15-27},

title = {Generalization of a problem of Diophantus},

url = {http://eudml.org/doc/206559},

volume = {65},

year = {1993},

}

TY - JOUR

AU - Andrej Dujella

TI - Generalization of a problem of Diophantus

JO - Acta Arithmetica

PY - 1993

VL - 65

IS - 1

SP - 15

EP - 27

LA - eng

KW - perfect squares; Fibonacci numbers; property of Diophantus

UR - http://eudml.org/doc/206559

ER -

## References

top- [1] J. Arkin and G. E. Bergum, More on the problem of Diophantus, in: Applications of Fibonacci Numbers, A. N. Philippou, A. F. Horadam and G. E. Bergum (eds.), Kluwer, Dordrecht, 1988, 177-181. Zbl0649.10011
- [2] A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1966.
- [3] H. Davenport and A. Baker, The equations 3x² - 2 = y² and8x² - 7 = z², Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137.
- [4] A. Dujella, One Diofant's problem and Fibonacci's numbers, Matematika 19 (3) (1990), 45-52 (in Croatian).
- [5] A. Dujella, Generalization of a Diophantine problem, Matematika 20 (1) (1991), 22-29 (in Croatian).
- [6] B. W. Jones, A variation on a problem of Davenport and Diophantus, Quart. J. Math. Oxford Ser. (2) 27 (1976), 349-353. Zbl0332.10008
- [7] C. Long and G. E. Bergum, On a problem of Diophantus, in: Applications of Fibonacci Numbers, A. N. Philippou, A. F. Horadam and G. E. Bergum (eds.), Kluwer, Dordrecht, 1988, 183-191. Zbl0649.10006
- [8] S. Vajda, Fibonacci & Lucas Numbers, and the Golden Section: Theory and Applications, Horwood, Chichester, 1989.
- [9] I. M. Vinogradov, Elements of Number Theory, Dover, New York, 1954 Zbl0057.28201

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