MathGroup Archive 2012

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primitive root error

  • To: mathgroup at
  • Subject: [mg128084] primitive root error
  • From: Dan Dubin <ddubin at>
  • Date: Fri, 14 Sep 2012 00:24:35 -0400 (EDT)
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The number theoretic function PrimitiveRoot[n]  is supposed to give the 
smallest generator for the multiplicative group of integers module n 
relatively prime to n.  However, Mathematica 8  says that
PrimitiveRoot[18] equals 11. This is incorrect. While this is a 
generator, it is not the smallest generator of the group. The correct 
answer is 5:

In[1]:= Table[Mod[5^n, 18], {n, 0, 6}]

Out[1]= {1, 5, 7, 17, 13, 11, 1}

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