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Math Help - Modular Arithmetic

  1. #1
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    Modular Arithmetic

    Hi Guys,

    Having some trouble with basic modular arithmetic, most of the materials i have dont seem to be helping..

    a simple question 2 mod 10 = 2.. how did they get = 2?

    3 mod 18 = 3, could you please explain the process
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  2. #2
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    Quote Originally Posted by extatic View Post
    Hi Guys,

    Having some trouble with basic modular arithmetic, most of the materials i have dont seem to be helping..

    a simple question 2 mod 10 = 2.. how did they get = 2?

    3 mod 18 = 3, could you please explain the process
    Definition a=b\!\!\pmod n\Longleftrightarrow n\mid (a-b)\Longrightarrow a-b=kn , when all the letters

    here symbolize integer numbers.

    Thus, 2=2\!\!\pmod{10} because 10\mid(2-2=0)\,,\,\,0=10\cdot 0 , and etc.

    A less trivial example: 11=47\!\!\pmod{18}\,\,because\,\,11-47=-36=18\cdot (-2)


    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    Definition a=b\!\!\pmod n\Longleftrightarrow n\mid (a-b)\Longrightarrow a-b=kn , when all the letters

    here symbolize integer numbers.

    Thus, 2=2\!\!\pmod{10} because 10\mid(2-2=0)\,,\,\,0=10\cdot 0 , and etc.


    A less trivial example: 11=47\!\!\pmod{18}\,\,because\,\,11-47=-36=18\cdot (-2)


    Tonio
    Thank you Tonio,

    what if b (mod n) is only given, not a ??
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  4. #4
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    Quote Originally Posted by extatic View Post
    Thank you Tonio,

    what if b (mod n) is only given, not a ??

    b\!\!\pmod n hasn't much meaning beyond indicating that we're considering an element b modulo some integer n...

    Tonio
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  5. #5
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    I'd like to add to tonio's reply. Programmers use b (mod n) to represent the remainder upon dividing b by n. For example, 7 (mod 5) equals 2, since 7/5 = 1, with remainder 2. See , for example, section 3.4 of Concrete Mathematics by Graham, Knuth and Patashnik.
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  6. #6
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    Thank you to you both

    Petek thank you for that..
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  7. #7
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    If this helps anyone,

    2648 (mod 7)

    2648 / 7 = 378.28...........
    378 x 7 = 2646

    2648 - 2646 = 2

    2468 (mod 7) = 2

    thanks for the help guys
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