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}