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Math Help - Gauss Lemma (Number Theory)

  1. #1
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    Gauss Lemma (Number Theory)

    Use Gauss Lemma (Number theory) to calculate the Legendre Symbol (\frac{6}{13}).

    I know how to use Gauss Lemma. However we use the book: Ireland and Rosen. They define Gauss Lemma as:

    (\frac{a}{p})=(-1)^n. They say: Let \pm m_t be the least residue of ta, where m_t is positive. As t ranges between 1 and \frac{(p-1)}{2}, n is the number of minus signs that occur in this way. I don't understand how to use this form of Gauss's Lemma
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  2. #2
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    Quote Originally Posted by mathsss2 View Post
    Use Gauss Lemma (Number theory) to calculate the Legendre Symbol (\frac{6}{13}).

    I know how to use Gauss Lemma. However we use the book: Ireland and Rosen. They define Gauss Lemma as:

    (\frac{a}{p})=(-1)^n. They say: Let \pm m_t be the least residue of ta, where m_t is positive. As t ranges between 1 and \frac{(p-1)}{2}, n is the number of minus signs that occur in this way. I don't understand how to use this form of Gauss's Lemma
    In \{ 6,12,18,24,30,36\} the corresponding remainders are \{6, -1, 5, -2, 4, -3 \}.
    There are 3 negative signs.
    Therefore, (6/13) = (-1)^3 = -1.
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