A number raised to one half its power is a square root.................so.............9..........to the one half power.....................as in 1/2............is 3............it is the square root of 9.................why are the zeros along the north - south line...........of 1/2.............what does a square root got to do with anything..........

On the face of it, this may not seem surprising, but I would stress that there is no apparent reason why trying to solve the equation

X 2 ≡ n mod p

should have anything to do with p modulo 4n. Thirty years after I first learnt how to prove this theorem, it still seems miraculous to me.