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Modular arithmetic

  1. Feb 5, 2009 #1
    i might be making it up, but i am confused.

    can we say:

    [tex]x\equiv[/tex]2 (mod k)
    [tex]x\equiv[/tex]2 (mod m)
    hence
    [tex]x\equiv[/tex]2 (mod km) by km i mean k multiplied by m.

    if not, what is the result? or can it be found?

    thank you in advance.
     
  2. jcsd
  3. Feb 5, 2009 #2

    Office_Shredder

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    No.

    k=4
    m=8
    x=10
    x=2(mod 4) and x=2(mod 8) but x=10(mod 32)

    In general, if you have something mod m and something mod k, and want to discuss what happens mod mk, then you need a condition on m and k being coprime, or something similar.
     
  4. Feb 5, 2009 #3
    thank you for your answer.

    i think i found sth:

    say (k,m) = 1

    x=a (mod k)
    x=a (mod m)

    x=kt+a and x=my+a
    kt=my
    t=mb
    y=kb

    then x=kmb+a
    x-a=kmb
    x-a=0 (mod km)
    x=a (mod km)

    it is valid, isnt it? any counterexamples?
     
  5. Feb 5, 2009 #4

    Office_Shredder

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    That looks pretty good to me
     
  6. Feb 5, 2009 #5
    :) then my problem is solved. now i should get back to work.
     
  7. Feb 5, 2009 #6

    HallsofIvy

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    Yeah, I hate when that happens!:tongue2:
     
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