Gauss's Lemma (number Theory) - Statement of The Lemma

Statement of The Lemma

For any odd prime p let a be an integer that is coprime to p.

Consider the integers

and their least positive residues modulo p. (These residues are all distinct, so there are (p−1)/2 of them.)

Let n be the number of these residues that are greater than p/2. Then

where (a/p) is the Legendre symbol.

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