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On the least quadratic non-residue

Published online by Cambridge University Press:  24 October 2008

H. J. Godwin
Affiliation:
University College of Swansea

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
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

(1)Burgess, D. A.Mathematika, 4 (1957), 106112.CrossRefGoogle Scholar
(2)Leveque, W. J.Topics in number theory, vol. I (Addison-Wesloy, Reading, Mass. 1956).Google Scholar