Re: primitive root error

*To*: mathgroup at smc.vnet.net*Subject*: [mg128181] Re: primitive root error*From*: Dana DeLouis <dana01 at me.com>*Date*: Fri, 21 Sep 2012 04:15:25 -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 ... Hi. Trying to read up on the subject I noticed this interesting note in Mathworld. It mentions that the program may not return the smallest solution if the number is composite (ie 18 ) Copy=85 A primitive root of a number (but not necessarily the smallest primitive root for composite ) can be computed inMathematica using PrimitiveRoot[n]. http://mathworld.wolfram.com/PrimitiveRoot.html = = = = = = = = = = HTH :>) Dana DeLouis Mac & Mathematica 8 = = = = = = = = = = On Friday, September 14, 2012 12:16:47 AM UTC-4, 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}