Note on the cubic residues. (English) Zbl 0932.11070

The paper gives a simple characterization for the cubic residues modulo \(p\), \(p\) a prime. These criteria are corollaries of Theorem 1, which deals with the decomposition of a number into 3 prime ideals in a certain algebraic number field.
Reviewer: J.Hančl (Ostrava)


11R18 Cyclotomic extensions
11A15 Power residues, reciprocity
Full Text: EuDML


[1] H. Davenport: Multiplicative Number Theory. Markham Publishing Company, Chicago, 1967. · Zbl 0159.06303
[2] K. Ireland, M. Rosen: A Classical Introduction to Modern Number Theory. Springer-Verlag New York Inc. 1982. · Zbl 0482.10001
[3] S. Jakubec: Criterion for 3 to be eleventh power. Acta Mathematica et Informatica Universitatis Ostraviensis 3 (1995) 37-43. · Zbl 0876.11002
[4] W. Narkiewicz: Elementary and Analytic Theory of Algebraic Numbers. PWN-Polish Scientific Publishers Warszawa, Springer Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong, Second Edition 1990. · Zbl 0717.11045
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