primitive root error
- To: mathgroup at smc.vnet.net
- Subject: [mg128084] primitive root error
- From: Dan Dubin <ddubin at ucsd.edu>
- 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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