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    Use Gauss' Lemma to show that 17 is a quadratic residue module 19.

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    6. Use Gauss' Lemma to show that 17 is a quadratic residue module 19.

    Please see attached.

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    Problem #6
    Proof:
    From Gauss's Lemma, we know that . We also know , so we have . Thus is a quadratic residue of .

    Problem #7
    Proof:
    According to the Quadratic Reciprocity Law, for any two odd primes and , we have

    If ...

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