prime number algorithm

khotsofalang

i am sorry guys, the last time i posted this problem it was completely different but this time if we
Let x₁²+x₂²=1 be a unit circle upon a finite field Zp where p is prime. Is there any algorithm which can give all the possible solutions (x₁,x₂) an element of Zp*Zp as well as the total number of such solutions? If exists, what is the complexity of it?

CRGreathouse

You could check all possibilities. That takes something like O(p^2 log^2 p).

Now you just need a *good* way to solve it.

khotsofalang

all right, but what i actually need is that good way of solving it

khotsofalang

i need a solution to such an equation for stregthening my extended essay,anibody with a gud way of solving it?