Complete Legendre-symbol sum
= Complete Legendre-symbol sum
For every odd prime $p$,
$$
\sum_{x\in\mathbb F_p}\left(\frac xp\right)=0.
$$
Multiplication by a quadratic nonresidue permutes $\mathbb F_p$ and negates every term.
= Complete Legendre-symbol sum
For every odd prime $p$,
$$
\sum_{x\in\mathbb F_p}\left(\frac xp\right)=0.
$$
Multiplication by a quadratic nonresidue permutes $\mathbb F_p$ and negates every term.