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The Algebra of the eth Power Residues
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The main object of the present paper is to show that the algebra of the Gaussian periods is identical with the algebra of the eth power residues mod p where p is a prime and e is a divisor of p-1. This algebra is obviously a particular case of the algebra of the eth power residues mod N where N is any integer. Since the system of residue classes mod N is abstractly identical with a cyclic group of order N, the above algebra may be interpreted to be the algebra of the eth power residues connected with a cyclic group of order N. It is therefore natural to enquire whether there is a similar algebra connected with any finite Abelian group. We shall however show by means of an example that this is not the case.
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