Congruence condition for two to be a quadratic residue

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Contents

1 Statement
2 Related facts
- 2.1 Similar facts
- 2.2 Applications

Statement

Suppose $\text{[math]}$ is an odd prime. Then:

$\text{[math]}$ is a quadratic residue modulo $\text{[math]}$ if and only if $\text{[math]}$ , i.e., $\text{[math]}$ or $\text{[math]}$ .
$\text{[math]}$ is a quadratic nonresidue modulo $\text{[math]}$ if and only if $\text{[math]}$ , i.e, $\text{[math]}$ or $\text{[math]}$ .

Related facts

Similar facts

Applications

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