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