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?

Thanks.