Review Note

Sommes de Gauß. On pose \(S(a) = \displaystyle \sum_{\bar x \in\mathbb Z/p\mathbb Z} \exp\left(\frac {2i\pi ax^2} p\right)\). Montrer que \({{c1::(S(1))^2 = (-1)^{\frac {p-1} 2 } p}}\).
\[{{c2::p = |S(1)|^2 = S(1)\overline {S(1)} = S(1)S(-1) = \left( \frac {-1} p \right)(S(1))^2}}\]