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A quadratic partition of primes $ \equiv 1$ $ ({\rm mod}\ 7)$


Author: Kenneth S. Williams
Journal: Math. Comp. 28 (1974), 1133-1136
MSC: Primary 10A40
DOI: https://doi.org/10.1090/S0025-5718-1974-0345902-2
MathSciNet review: 0345902
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Abstract: The solutions of a quadratic partition of primes $ p \equiv 1 \pmod 7$, in terms of which the author and P. A. Leonard have given the cyclotomic numbers of order seven and also necessary and sufficient conditions for 2, 3, 5 and 7 to be seventh powers $ \pmod p$, are obtained for all such primes $ < 1000$.


References [Enhancements On Off] (What's this?)

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  • [7] K. G. REUSCHLE, "Zerfällung aller Primzahlen innerhalb des ersten Tausend in ihre aus siebenten Wurzeln der Einheit gebildeten complexen Primfactoren," Monatsh. Kl. Preuss. Akad. Wiss. Berlin, v. 1859, pp. 694-697.

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DOI: https://doi.org/10.1090/S0025-5718-1974-0345902-2
Article copyright: © Copyright 1974 American Mathematical Society

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