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Math Help - how to slove the congruence s.t x^2+1=0 mod 5 ??

  1. #1
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    how to slove the congruence s.t x^2+1=0 mod 5 ??

    how to slove the congruence such that

    <br />
x^{2}+1\equiv 0  (\bmod 5)<br />

    cheers!
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  2. #2
    Super Member Deadstar's Avatar
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    Since you're working in mod 5 you just need to check the values 0,1,2,3,4.

    For 0 we have, 0^2 + 1 = 1
    For 1 we have, 1^2 + 1 = 2
    For 2 we have, 2^2 + 1 = 5 = 0 mod 5
    For 3 we have, 3^2 + 1 = 10 = 0 mod 5
    For 4 we have, 4^2 + 1 = 17 = 2 mod 5

    So x = 2 or 3.

    Do you understand what mod 5 means?
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  3. #3
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    if the modulo here is 7. shall i only need to consider the values 0 up to 6?
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  4. #4
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    Hi

    Quote Originally Posted by xixihaha View Post
    if the modulo here is 7. shall i only need to consider the values 0 up to 6?
    Yep, that is correct.

    Yours
    Rapha


    Edit:

    see if the question is like x^2-1= 0 mod 5
    (edited a "0" )

    Yes you can use the same method.
    Last edited by Rapha; May 18th 2009 at 06:38 AM.
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  5. #5
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    thank you~i understand now.

    see if the question is like
    <br />
x^{2}-1\equiv 0 (\bmod 5)<br />
    can i use that method to solve the problem??
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  6. #6
    Super Member Deadstar's Avatar
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    Yep. Just plug in the values of x you can use and mod the answer by 5 until its between (or equal to) 0 and 4. Can you figure out which values of x will give x^2 - 1 = 0 mod 5? Hint: there's two of them.
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  7. #7
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    <br />
(x-1)(x+1)\equiv 0 (\bmod 5)<br />

    <br />
x\equiv 1 (\bmod 5)<br />

    <br />
x\equiv -1 (\bmod 5)<br />

    so x =0,1

    am i right?
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  8. #8
    Super Member Deadstar's Avatar
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    I think you've mistyped there. Should be 'so x = -1,1'

    But -1 = 4 mod 5 so the answer is x = 1 and 4.

    Test this by putting the values into x^2 - 1.

    x=0 gives 0-1 = -1 = 4 mod 5 (since -1 + 5 = 5)
    x=1 gives 1-1 = 0.
    x=2 gives 4-1 = 3.
    x=3 gives 9-1 = 8 = 3 mod 5 (since 8 - 3 = 5)
    x=4 gives 16-1 = 15 = 0 mod 5 (since 15 - 5 - 5 - 5 = 0)

    This confirms that 1 and 4 are the correct answers.
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  9. #9
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    oh yes. you are right. im quite clear now.
    last,i'll say thank you to Rapha and Deadstar for helping me.
    cheers.
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