# 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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Please see the attachment.

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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This solution is comprised of a detailed explanation to use Gauss' Lemma to show that 17 is a quadratic residue module 19.

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