[Math] Chinese remainder theorem for three equations

chinese remainder theoremcongruenceselementary-number-theorymodular arithmetic

Is there a straightforward approach for solving the Chinese Remainder Theorem with three congruences?

$$x \equiv a \bmod A$$

$$x \equiv b \bmod B$$

$$x \equiv c \bmod C$$

Assuming all values are positive integers, not necessarily prime, but sometimes solutions do exist.

Best Answer

You solve the first two, then take that result and the remaining equation and you solve those two.