Formulas For The Square Root Modulo p
Kedlaya, Kiran S., Kopparty, Swastik · arXiv (Cornell University) · 2011
A method of constructing specific polynomial representations $f(x)$ over the finite field $\mathbb{F}_p$ of the square roots function modulo a prime $p = 2^kn + 1$, $n$ odd, is presented. The formulas for the cases $k = 2$, $3$ and $4$ are given.