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Thread: For what primes p...

  1. March 28th 2010, 07:24 PM #1
    NikoBellic
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    For what primes p...

    For what primes p (not 2 or 5) do we have

    (10/p) = 1?
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  2. March 28th 2010, 07:38 PM #2
    chiph588@
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    Quote Originally Posted by NikoBellic View Post
    For what primes p (not 2 or 5) do we have

    (10/p) = 1?
    \left(\frac{10}{p}\right) = \left(\frac{2}{p}\right) \left(\frac{5}{p}\right)

    So if \left(\frac{10}{p}\right)=1 , then \left(\frac{2}{p}\right)=\left(\frac{5}{p}\right)= 1 or \left(\frac{2}{p}\right)=\left(\frac{5}{p}\right)=-1

    Now you can use quadratic reciprocity to find \left(\frac{2}{p}\right) and \left(\frac{5}{p}\right) .
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  3. March 29th 2010, 06:08 AM #3
    pollardrho06
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    Nice!
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