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Math Help - roots

  1. #1
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    roots

    How many roots has the polynomial x^2 - 5 v Z<br />
257?
    I know it can be 0,1 or 2.

    thank you
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  2. #2
    MHF Contributor

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    Quote Originally Posted by putnam120 View Post
    I'm not sure I understand the question the way it is written. Are you trying to ask:
    How many solutions does x^2-5\equiv 0\bmod{257} have?

    If so then the answer is 2 since 257 is prime. (Note: If p is prime, then \mathbb{Z}_p is a field.)
    actually there's no solution! applying QRT gives us: \left(\frac{5}{257} \right)=\left(\frac{257}{5} \right)=\left(\frac{2}{5} \right)=-\left(\frac{5}{2} \right)=-\left(\frac{1}{2} \right)=-1.

    by the way, questions like this one should be posted in the number theory subforum.
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  3. #3
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    Oh whoops totally forgot about that. I'll remove the previous post.
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