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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Consecutive power residues or nonresidues
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by J. R. Rabung and J. H. Jordan PDF
Math. Comp. 24 (1970), 737-740 Request permission

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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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 737-740
  • MSC: Primary 10.06
  • DOI: https://doi.org/10.1090/S0025-5718-1970-0277469-8
  • MathSciNet review: 0277469