Could you please state the problem clearly?
It's a little confusing right now.
I have to solve a system using The Chinese Reminder Theorem.
It has two equations:
x= +-4 mod 31
x= +- 22 mod 53
I've got N = 1643 And a1N1K1 + a2N2K2 = +-5088+-8184.
I know how to find the first two solutions:
x1 = 5088 + 8184 (mod 1643)
x2 = 8184 - 5088 (mod 1643)
but how about x3, x4?