Quote:
Originally Posted by bhelmes
For mathematical curosity and practical use:
Is it possible to calculate the square root of a quadratic residium by using the tangens function ?

I am unaware of any such method.
For primes p congruent to 1 (mod 4) I don't know of any faster way than factoring x
^{2}  r over the finite field with p elements. In PariGP sqrt(Mod(r, p)) will return the square root in (0,p/2) if p is prime and r is a quadratic residue (mod p).