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MathGroup Archive 1999

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RE: Finding a relative prime

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19694] RE: [mg19682] Finding a relative prime
  • From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
  • Date: Sat, 11 Sep 1999 16:36:02 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Timur Tabi  wrote:
------------------------
I'm using Mathematica 3.0 for the Mac, and I'm trying to figure out how to
get it to pick a random number that is relatively prime to another number,
p-1, where p is prime.  In other words, pick a random number k such that 
1) k is between 2 and p-1, 
2) k is relatively prime to p-1.

------------------------

This should work:


PickNumber[p_?PrimeQ]:=
  Module[{tst,k},
    While[tst=!=1,
      k=Random[Integer,{2,p-2}];
      tst=GCD[k,p-1]
    ];
    k
  ]


However, when p=2,3,5,7
there is only one integer less than (p-1)
that is relatively prime to (p-1), and that doesn't 
allow for a very random outcome.

--------------------
Regards,
Ted Ersek

For Mathematica tips, tricks see 
http://www.dot.net.au/~elisha/ersek/Tricks.html


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