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Re: Re: Finding a relative prime


Hello,

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, and 2) k is relatively prime to p-1.
How can I do that in Mathematica 3.0?


Ken Levasseur used in his solution FixedPoint.

relprime[p_] := 
  FixedPoint[Random[Integer, {2, p - 2}] &, p - 1, 
    SameTest -> ((GCD[p - 1, #2] == 1) &)]

You can also use a recursive function:

Clear[f];
f[p_] /; PrimeQ[p] && p > 3 := 
   (If[GCD[#1, p - 1] === 1, #1, f[p]] & )[Random[Integer, {2, p - 2}]]




Frans Martens
Eindhoven University of Technology
Faculty of Mathematics and Computer Science
P.O.Box 513
5600 MB Eindhoven The Netherlands
Telephone -31402474280 
Telefax -31402436685
E-mail fransm at win.tue.nl


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