Definition:Legendre Symbol/Also presented as

Legendre Symbol: Also presented as

For a given odd prime $p$, the Legendre symbol can be treated as a mapping:

$f_p: \Z \to \set {-1, 0, 1}$

Some sources define it casually as a mapping $f : \mathbb P_{\ge 3} \times \Z \to \set {-1, 0, 1}$.

The only really complicated thing about this is its notation.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Legendre symbol
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Legendre symbol