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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: <IMG WIDTH="17" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img5.gif" ALT="$k$">th-power character, <IMG WIDTH="17" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$k$">th-power residues, <IMG WIDTH="17" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$k$">th-power nonresidues, <IMG WIDTH="17" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img4.gif" ALT="$k$">th-power class
Article copyright: © Copyright 1970 American Mathematical Society