Legendre Symbol/Examples/3 over 7

Example of Use of Legendre Symbol

$\paren {\dfrac 3 7} = -1$

Proof

From Quadratic Residue Examples: $7$:

The set of quadratic residues modulo $7$ is:

$\set {1, 2, 4}$

That is, $3$ is not a quadratic residue of $7$.

Hence the result by definition of Legendre symbol.

$\blacksquare$

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