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MathGroup Archive 1999

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Re: MultiplicativeOrder[k,n] ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18419] Re: [mg18373] MultiplicativeOrder[k,n] ?
  • From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
  • Date: Wed, 7 Jul 1999 00:11:14 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

a=b mod n means that a-b is divisible by n (a,b,n integers). This is the 
basis of "modular arithmetic" invented by Gauss and discussed in every book
on elementary number theory. For example, a famous result in this area is
Fermat's little theorem:
if p is a prime and does not divide a then a^(p-1)=1 mod p. In Mathematica'S
notation this becomes Mod[a^(p-1),p]==1 or PowerMod[a,p-1,p]==1 if
GCD[a,p]==1. This implies that MultiplicativeOrder[a,p] divides p-1, e.g.
with a=2 and p=17

In[57]:=
MultiplicativeOrder[2, 17]
Out[57]=
8
--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp


----------
>From: piovere at flash.net (Rob Peterson)
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg18419] [mg18373] MultiplicativeOrder[k,n] ?
>Date: Thu, Jul 1, 1999, 3:13 AM
>

> I am trying to figure out what MultiplicativeOrder[k,n] is. The book
> says this function gives the smallest integer m such that k^m = (3
> lines as if this is a definition) 1 mod n.  I understand what Mod[k,n]
> means but I dont' understand what "1 mod n" means.  Could someone
> please help me - I've found nothing in the math books on the subject.
>
> Thanks, Rob


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