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Mathematics of Computation

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Numbers having $ m$ small $ m$th roots mod $ p$

Author: Raphael M. Robinson
Journal: Math. Comp. 61 (1993), 393-413
MSC: Primary 11A07; Secondary 11A15, 11L10, 11R18
MathSciNet review: 1189522
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Abstract: Here are two typical results about the numbers mentioned in the title: If p is a prime such that $ p \equiv 1 \pmod 6$ and $ p > 67$, then there are exactly six numbers $ \bmod\;p$, each of which has six sixth roots less than $ 2\sqrt {3p} $ in absolute value. If p is a prime such that $ p \equiv 1 \pmod 8$, then there is at least one number $ \bmod\;p$ which has eight eighth roots less than $ {p^{3/4}}$ in absolute value.

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Article copyright: © Copyright 1993 American Mathematical Society

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