
primitive root error
Posted:
Sep 14, 2012 12:15 AM


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}

