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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)
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> 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}