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Unique determination of cyclotomic numbers of order five. (English) Zbl 0577.12014

The authors give a complete solution to the problem of determining the cyclotomic numbers of order five over a finite field with \(p^ a\) elements, where \(a\geq 1\) and p is a prime congruent to 1 modulo 5.
Reviewer: K.S.Williams

MSC:

11T22 Cyclotomy
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References:

[1] DICKSON, L.E.: Cyclotomy, higher congruences, and Waring’s problem. Amer. J. Math. 57 (1935), 391-424 · Zbl 0012.01203 · doi:10.2307/2371217
[2] KATRE, S.A. and RAJWADE, A.R.: Complete solution of the cyclotomic problem inF q for any prime modulus 1, q=p?, p?1 (mod 1). Acta Arith. (to appear in Nr. 45) · Zbl 0525.12015
[3] PARNAMI, J.C., AGRAWAL, M.K. and RAJWADE, A.R.: Jacobi sums and cyclotomic numbers for a finite field. Acta Arith. 41 (1982), 1-13 · Zbl 0491.12019
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