The cyclotomic numbers of order seven are given in terms of the solutions of a certain system of three quadratic diophantine equations. This is analogous to L. E. Dickson's evaluation of the cyclotomic numbers of order five, and is a convenient approach for applications to the theory of power residues.

Additional Metadata
Keywords Cyclotomic numbers, Dickson-Hurwitz sums, Jacobi sums
Persistent URL dx.doi.org/10.1090/S0002-9939-1975-0371868-8
Journal Proceedings of the American Mathematical Society
Citation
Leonard, P.A. (Philip A.), & Williams, K.S. (1975). The cyclotomic numbers of order seven. Proceedings of the American Mathematical Society, 51(2), 295–300. doi:10.1090/S0002-9939-1975-0371868-8