Linear congruence equation

The solution of linear congruence equations can be decomposed into several linear congruence equations. For example, for linear congruence equations:

2x ≡ 2 (mod 6)

3x 2(mod 7)

2x ≡ 4 (Module 8)

Solve the first equation and get x ≡ 1 (mod 3), so let x = 3k+ 1, and the second equation becomes:

9k ≡？ 1 (clause 7)

The solution is k ≡ 3 (mod 7). Then, let k = 7l+3, and the third equation can be changed to:

42l ≡？ 16 (section 8)

Solution: l ≡ 0 (mod 4), that is, l = 4m. If you substitute the original expression, there is x = 21(4m)+10 = 84m+10, which is the solution:

X10 (model year 84)

We need the remainder theorem in China's number theory to know whether there is a solution in general and how to get it.