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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Consecutive power residues or nonresidues

Authors: J. R. Rabung and J. H. Jordan
Journal: Math. Comp. 24 (1970), 737-740
MSC: Primary 10.06
MathSciNet review: 0277469
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Abstract: For any positive integers $ k$ and $ l$, A. Brauer [1] has shown that there exists a number $ z(k,l)$ such that, for any prime number $ p > z(k,l)$, a sequence of $ l$ consecutive numbers occurs in at least one $ k$th-power class modulo $ p$. For particular $ k$ and $ l$, one is sometimes able to find a least bound, $ \Lambda *(k,l)$, before, or at which, the first member of such a sequence must appear. In this paper, we describe a method used to compute $ \Lambda *(8,2)$ and $ \Lambda *(3,3)$.

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Keywords: $ k$th-power character, $ k$th-power residues, $ k$th-power nonresidues, $ k$th-power class
Article copyright: © Copyright 1970 American Mathematical Society