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Explicit criteria for quintic residuacity. (English) Zbl 0341.10004


MSC:

11A15 Power residues, reciprocity
11T22 Cyclotomy
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References:

[1] C. E. BICKMORE, ”On the numerical factors of \( {a^n - 1}\). II,” Messenger Math., v. 26, 1897, pp. 1-38.
[2] A. J. C. CUNNINGHAM & T. GOSSET, ”4-tic and 3-tic residuacity tables,” Messenger Math., v. 50, 1920, pp. 1-30. · JFM 47.0125.02
[3] L. E. Dickson, Cyclotomy, Higher Congruences, and Waring’s Problem, Amer. J. Math. 57 (1935), no. 2, 391 – 424. · Zbl 0012.01203 · doi:10.2307/2371217
[4] P. D. T. A. Elliott, A problem of Erdős concerning power residue sums, Acta Arith. 13 (1967/1968), 131 – 149. · Zbl 0159.06401
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[9] Emma Lehmer, Artiads characterized, J. Math. Anal. Appl. 15 (1966), 118 – 131. · Zbl 0151.02704 · doi:10.1016/0022-247X(66)90145-4
[10] Emma Lehmer, On the divisors of the discriminant of the period equation, Amer. J. Math. 90 (1968), 375 – 379. · Zbl 0169.06401 · doi:10.2307/2373534
[11] Horst von Lienen, Primzahlen als achte Potenzreste, J. Reine Angew. Math. 266 (1974), 107 – 117 (German). · Zbl 0279.10003 · doi:10.1515/crll.1974.266.107
[12] G. B. Mathews, Theory of numbers, 2nd ed, Chelsea Publishing Co., New York, 1961.
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