# Why is the Legendre symbol not defined for $p = 2$ (even prime)?

Why is the Legendre symbol not defined for $p = 2$ (even prime) ?

According to the definition of the Legendre symbol $$\left(\frac a p\right)$$ it is defined for an odd prime $p$ only. Even thus the case where $p = 2$ is an even prime is not particularly interesting, why are the restriction made that $p$ must be an odd prime ?