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.
Read more about this topic: Gauss's Lemma (number Theory)
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