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Pairs of Consecutive Power Residues

Published online by Cambridge University Press:  20 November 2018

D. H. Lehmer ,
Emma Lehmer  and
W. H. Mills
D. H. Lehmer
Affiliation:
University of California, Berkeley Yale University
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Until recently none of the numerous papers on the distribution of quadratic and higher power residues was concerned with questions of the following sort: Let k and m be positive integers. According to a theorem of Brauer (1), for every sufficiently large prime p there exist m consecutive positive integers r, r + 1 , . . . , r + m — 1, each of which is a kth power residue of p. Let r(k, m, p) denote the least such r.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 172 - 177
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Brauer, Alfred, Ueber Sequenzen von Potenzresten, Akad. der Wiss., Berlin, Sitz. (1928), 9-16.Google Scholar
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