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Evaluation of Certain Legendre Symbols

David Angell
The American Mathematical Monthly
Vol. 119, No. 8 (October 2012), pp. 690-693
DOI: 10.4169/amer.math.monthly.119.08.690
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.119.08.690
Page Count: 4
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Evaluation of Certain Legendre Symbols
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Abstract

Abstract We state and prove an apparently hitherto unrecorded evaluation of certain Legendre symbols: if p is prime, p ≠ 2, and ab = p − 1, then the Legendre symbol \documentclass{article} \pagestyle{empty}\begin{document} $\legendre{b}{p}$ \end{document} is given by \documentclass{article} \pagestyle{empty}\begin{document} $$\legendre{b}{p}=(-1)^{\lceil a/2\rceil\lfloor b/2\rfloor}.$$ \end{document}

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