How to rewrite this correctly: There are several ways to show how the randomized primality test works for N = 561 with several choices of A. One way is to use the fact that if N is prime, then for any integer A coprime to N, we have that A^(N-1) = 1 (mod N). Thus, we can simply check whether A^560 = 1 (mod 561) for various choices of A. For example, let A = 2. Then we have A^560 = 2^560 = 1 (mod 561). Therefore, we would conclude that 561 is probably prime. We can also use the fact that if N is composite, then for any integer A coprime to N, we have that A^(N-1) != 1 (mod N). Thus, we can simply check whether A^560 != 1 (mod 561) for various choices of A. For example, let A = 3. Then we have A^560 = 3^560 = 1 (mod 561). Therefore, we would conclude that 561 is composite. The randomized primality test for N = 561 with several choices of A is as follows: First, we choose a random integer A between 1 and 561. Then, we compute A^560 (mod 561). If A^560 = 1 (mod