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MathGroup Archive 1999

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Re: MultiplicativeOrder[k,n] ?

  • To: mathgroup at
  • Subject: [mg18404] Re: MultiplicativeOrder[k,n] ?
  • From: "David Bailey" <db at>
  • Date: Wed, 7 Jul 1999 00:11:04 -0400
  • Organization: University of Salford, Salford, Manchester, UK
  • References: <7lceij$>
  • Sender: owner-wri-mathgroup at

Rob Peterson <piovere at> wrote in message
news:7lceij$1j5 at
> 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.

Here is an example which should make this clear:

MultiplicativeOrder[3, 11]


Table[Mod[3^k, 11], {k, 1, 10}]

{3, 9, 5, 4, 1, 3, 9, 5, 4, 1}

Thus the multiplicative order of 3 Mod 11 is 5, which means that the first 1
in the above table occurs in position 5.

a (3 lines) b mod n

means Mod[a,n]==Mod[b,n]

I hope this helps,

David Bailey
Salford Software

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