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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

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}

**Follow-Ups**:**Re: primitive root error***From:*Andrzej Kozlowski <akozlowski@gmail.com>

**Re: primitive root error***From:*Bob Hanlon <hanlonr357@gmail.com>