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Math Help - Quadratic residue -5

  1. #1
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    Quadratic residue -5

    Hey, so the problem is to find all primes for which -5 is a quadratic residue.
    If one can tell me the answer I can probably prove it (using Gauss Lemma or Legendre symbol or so), but so far the primes seem to be randomly distributed.

    I have that -5 is a quadratic residue for p = 2, 3, 5 (trivial / exceptional cases)
    and for p = 7, 23, 29, 41, 43, 47, 61, 67...

    and -5 is a quadratic non-residue for p = 11, 13, 17, 19, 31, 37, 59...

    Now while writing this I noticed that its true for even 10th powers and false for odd 10th powers. Is that the solution?
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  2. #2
    MHF Contributor chiph588@'s Avatar
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  3. #3
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    How do you get
    \left(\frac{-1}{p}\right) =(-1)^{\frac{p-1}{2}} ?

    EDit: I found it on wiki, thanks a lot!
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Euler's Criterion.
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