Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T01:32:54.709Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

Extract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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