Re: primitive root error

*To*: mathgroup at smc.vnet.net*Subject*: [mg128096] Re: primitive root error*From*: daniel.lichtblau0 at gmail.com*Date*: Sat, 15 Sep 2012 03:38:39 -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*References*: <k2ub15$h9h$1@smc.vnet.net>

On Thursday, September 13, 2012 11:16:47 PM UTC-5, Dan Dubin wrote: > 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} Me, I'd call that a mistake in the documentation. Anyway, you can get the smallest by resorting to a crude, nay, barbaric tactic: invoke Wolfram|Alpha to find all the primitive roots. In[71]:= WolframAlpha["primitive roots of 18", "MathematicaResult"] Out[71]= {5, 11} Daniel Lichtblau Wolfram Research

**Follow-Ups**:**Re: primitive root error***From:*danl@wolfram.com

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