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Pairs of Consecutive Power Residues or Non-Residues

Published online by Cambridge University Press:  20 November 2018

J. H. Jordan
J. H. Jordan*
Affiliation:
Washington State University
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For a positive integer k and a prime p ≡ 1 (mod k), there is a proper subgroup, R, of the multiplicative group (mod p) consisting of the kth power residues (mod p). A necessary and sufficient condition that an integer t be an element of R is that the congruence xk ≡ t (mod p) be solvable. The cosets, not R, formed with respect to R are called classes of kth power nonresidues, and form with R a cyclic group of order k. Let ρ be a primitive kth root of unity and let S be a class of non-residues that is a generator of this cyclic group. There is a kth power character X (mod p) such that

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 310 - 314
Copyright
Copyright © Canadian Mathematical Society 1964

References

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