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Math Help - quadratic non residue

  1. #1
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    quadratic non residue

    Show that the smallest quadratic non residue of an odd prime p is itself prime. Hint: Assume to the contrary and use Legendre Symbols
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Assume not so let  n be the smallest QNR such that  n=ab . Then  -1=\left(\frac{n}{p}\right)=\left(\frac{ab}{p}\righ  t) = \left(\frac{a}{p}\right)\left(\frac{b}{p}\right) = (1)(1) = 1 since  a,b < n . Hence a contradiction.
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