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State/Half of nonzero residues are quadratic residues
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Proposition: (Half of nonzero residues are quadratic residues) Suppose that $p$ is an odd prime number. Then, among the $p-1$ nonzero residues mod $p$, precisely half (i.e., $(p-1)/2$) are quadratic residues.
Logical Connections
This statement logically relies on the following definitions and statements: Def/Prime number, Def/Quadratic residue, Def/Two to one, State/There are no zero divisors mod p, Def/Cardinality
The following statements and definitions rely on the material of this page: State/Eulers criterion
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