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Topic: primitive root error
Replies: 5   Last Post: Sep 21, 2012 4:21 AM

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Dan Dubin

Posts: 13
Registered: 3/26/09
primitive root error
Posted: Sep 14, 2012 12:15 AM
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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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