# Legendary Product

**Number Theory**Level 3

Let \( \left( \dfrac{a}{p} \right) \) denote the Legendre symbol.

If \( p = 2011\), find the value of \( \ \displaystyle \prod_{a = 1} ^{p - 1} \ \left( \dfrac{a}{p} \right)\).

Let \( \left( \dfrac{a}{p} \right) \) denote the Legendre symbol.

If \( p = 2011\), find the value of \( \ \displaystyle \prod_{a = 1} ^{p - 1} \ \left( \dfrac{a}{p} \right)\).

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