Linear congruence equations

The linear congruence equations are obtained by multiple linear congruence equations. The mathematical notation is the solution to the equation Ai*x≡bi (mod m) (1≤i≤n).

The complete works of the solution must be written in the form of X≡b (mod m), so we can solve all the linear congruence equations in turn.

Because X≡B1 (mod M1), so the x is written in x=b1+m1*t and substituting the second formula, you can get

A (b1+m1*t) ≡b2 (mod m2)

Organized to

A*M1*T≡B2-A*B1 (mod m2)

Then we can solve this one-time congruence equation. When GCD (M2,A*M1) cannot divide b2-a*b1, the original equations have no solution.

Linear congruence equations