How do you find the square root of a number mod a product of primes? I know that algorithms exist for finding the square root of a number mod a prime, such as tonelli-shanks, but I also know there must be an easier way to find the square roots mod pq where p and q are distinct primes.
The specific problem that I am trying to solve is "find all square roots of 1748 mod 11201. (Hint: 11201 = 103*107. 103 and 107 are both prime).