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  1. #1
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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. #2
    MHF Contributor chiph588@'s Avatar
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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. #3
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    Nice!
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