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Topic: primitive root error
Replies: 5   Last Post: Sep 21, 2012 4:21 AM

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 Dana DeLouis Posts: 107 Registered: 12/14/08
Re: primitive root error
Posted: Sep 21, 2012 4:21 AM

> 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

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HTH :>)
Dana DeLouis
Mac & Mathematica 8
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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
>
>
>
>
> In[1]:= Table[Mod[5^n, 18], {n, 0, 6}]
>
>
>
> Out[1]= {1, 5, 7, 17, 13, 11, 1}

Date Subject Author
9/14/12 Dan Dubin
9/15/12 daniel.lichtblau0@gmail.com
9/16/12 Andrzej Kozlowski
9/18/12 Daniel Lichtblau
9/21/12 Dana DeLouis