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On square values of quadratics

Published online by Cambridge University Press:  24 October 2008

D. Allison
D. Allison
Affiliation:
Department of Mathematics, University of Cape Town, 7700 Rondebosch, South Africa
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Let N be a positive integer. We enquire whether there is a quadratic f(t)=at2 + bt + c, not identically square, which takes square values for N consecutive integers t. In [1] it was shown that this was possible, in what we shall call the symmetric case, if N = 8. A better treatment of this case appears here, together with a discussion of the nonsymmetric case, where we may take N = 7. There is no evidence that these are the best possible results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 3 , May 1986 , pp. 381 - 383
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Allison, D.On certain simultaneous diophantine equations. Math. Colloq. Univ. Cape Town 11 (1977), 117–133.Google Scholar
[2]Nagell, T.Introduction to Number Theory (Almqvist and Wiksell, 1951).Google Scholar