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Mathematics of Computation

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Explicit criteria for quintic residuacity


Author: Kenneth S. Williams
Journal: Math. Comp. 30 (1976), 847-853
MSC: Primary 10A15
DOI: https://doi.org/10.1090/S0025-5718-1976-0412089-9
MathSciNet review: 0412089
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Abstract: Let p be a $ {\text{prime}} \equiv 1 \pmod 5$. Necessary and sufficient conditions are determined for the prime $ q(q \leqslant 19)$ to be a quintic residue of p. The results for $ q \leqslant 7$ are known, the rest are new.


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DOI: https://doi.org/10.1090/S0025-5718-1976-0412089-9
Keywords: Quintic residue, primitive root, f-nomial periods, period equation
Article copyright: © Copyright 1976 American Mathematical Society