How to find the sum: $\displaystyle \sum_{x=0}^{p-1} e^{2\pi i(ax^2+bx+c)/p}$ where p is prime ?
I'm sure I need to use this:
$\displaystyle \sum_{x=0}^{p-1} e^{2\pi i(x^2)/p}$ = $\sqrt{p}$ when $ p≡3(mod4)$ and $\sqrt{ip}$ when $ p≡1(mod4) $ and maybe I need to complete the square but I don’t know how to get the result