Weighted complete Legendre-symbol sum
= Weighted complete Legendre-symbol sum
For $T=\sum_{a=1}^{p-1}a(\frac ap)$, one has $T=0$ when $p\equiv1\pmod4$, and $T\equiv0\pmod p$ for every $p>3$.
= Weighted complete Legendre-symbol sum
For $T=\sum_{a=1}^{p-1}a(\frac ap)$, one has $T=0$ when $p\equiv1\pmod4$, and $T\equiv0\pmod p$ for every $p>3$.