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On the least quadratic non-residue

Published online by Cambridge University Press:  24 October 2008

H. J. Godwin
H. J. Godwin
Affiliation:
University College of Swansea
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Extract

If n(p) is the least quadratic non-residue of a given prime p then it is known ((1)) that n(p) = O(pα) for any α > 1/(4 √e). LeVeque ((2), page 122) gives the following bound with an explicit constant: n( p) < √ p for p ≠ 2, 3, 7, 23. In the present paper an elementary and self-contained proof is given of a result slightly stronger than LeVeque's. Some numerical results, which indicate the extent to which the result proved falls short of what actually obtains, are appended.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 3 , July 1965 , pp. 671 - 672
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

(1)Burgess, D. A.Mathematika, 4 (1957), 106–112.CrossRefGoogle Scholar
(2)Leveque, W. J.Topics in number theory, vol. I (Addison-Wesloy, Reading, Mass. 1956).Google Scholar