The problem I'm attempting to solve is:
Apply Gauss's Lemma to determine the primes of which -2 is a quadratic residue. I'm completely lost.
Using Gauss's Lemma to determine primes of a quadratic residue
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number-theory
quadratic-reciprocity
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0With the reciprocity law (See : https://en.wikipedia.org/wiki/Reciprocity_law) it would be much easier to find the desired primes. Is there a special reason you want a proof only with Gauss's Lemma ? – 2017-02-11
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0Gauss's Lemma states that for $ a, 2a, 3a, ..., \frac{p-1}{2}a $ we take the modulus p, and get a set of equations: $ a = r mod (p) $ $ 2a = r mod (p) $ $ .... $ $ \frac{p-1}{2}a = r mod (p) $ – 2017-02-11