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Modular Arithmetic game

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  • Kermit Rose
    Remember those arithmetical games played in high school Someone would tell you, Think of a number, add 3 multiply by 5, subtract 2 multiply by 2 subtract 1
    Message 1 of 1 , Dec 14, 2005
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      Remember those arithmetical games played in high school

      Someone would tell you,

      Think of a number,

      add 3

      multiply by 5,

      subtract 2

      multiply by 2

      subtract 1

      multiply by 4

      subtract 100

      divide by 40

      The result is your original number.


      Similar games are more mysterious in modular arithmetic.

      Select any odd prime, p > 5


      Do following in arithmetic mod p.



      Find inverse of 3 mod p.

      add (p+1)/2

      divide by 5

      add (p+1)/2

      subtract from p

      divide by 2

      add (p+1)/2

      multiply by 3

      add (p+1)/2

      result is 1.
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