Category:Legendre Symbol

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This category contains results about the Legendre symbol.
Definitions specific to this category can be found in Definitions/Legendre Symbol.

Let $p$ be an odd prime.

Let $a \in \Z$ be an integer.

The Legendre symbol $\paren {\dfrac a p}$ is defined as:

   \(\ds 0 \) if $a \equiv 0 \pmod p$      
   \(\ds +1 \) if $a$ is a quadratic residue of $p$      
   \(\ds -1 \) if $a$ is a quadratic non-residue of $p$