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I Points of a finite projective line

  1. Sep 14, 2016 #1
    I found in Thompson "From Error-Correcting to Sphere Packing and Simple Groups" this on page 131

    upload_2016-9-14_9-58-29.png

    How do you compute m/n in a finite field?

    Take the equivalence class 5 given above. Why does 2/5 and 18/22 give 5?

    thanks
     
  2. jcsd
  3. Sep 14, 2016 #2

    andrewkirk

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    The finite field being used is ##GF(23)## which is (isomorphic to) the set of integers modulo 23. Because 23 is prime, that is a field.

    2/5=5 because ##5\times 5=25=2\mod 23##
    18/22=5 because ##5\times 22=110=18\mod 23##

    If you are operating in a finite field of prime order ##p##, the multiplicative inverse of ##f## is the smallest positive solution ##x## of the equation ##xf=1+kp## for ##k## any non-negative integer.
     
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