Theorem: Let y be a quadratic residue in Z_N* where N=pq. There are exactly four integers x_1, x_2, x_3 and x_4 where 0 < x_1 < x_2 < N/2 < x_3 < x_4 < N such that y = x_i^2 mod N for i =1,2,3,4.

The above theorem simply say that the exactly two of the four roots must be greater than N/2.

Most paper will state that this result is well known, without provide any detail proof. How can we proof 0 < x_1 < x_2 < N/2 < x_3 < x_4 < N ?