Terminology, Data, and Two Statements of The Theorem
A quadratic residue (mod n) is any number congruent to a square (mod n). A quadratic nonresidue (mod n) is any number which is not congruent to a square (mod n). The adjective "quadratic" can be dropped if the context makes it clear that it is implied. When working modulo primes (as in this article), it is usual to treat zero as a special case. By doing so, the following statements become true:
Modulo a prime, there are an equal number of quadratic residues and nonresidues.
Modulo a prime, the product of two quadratic residues is a residue, the product of a residue and a nonresidue is a nonresidue, and the product of two nonresidues is a residue.
Read more about this topic: Quadratic Reciprocity
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