So I know that if all of your moduli are relatively prime to each other, you can simply apply the Chinese remainder theorem. However, what do you do if the moduli are not relatively prime?
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See General EASY CRT, or split the congruences into equivalent coprime congruences e.g. as here. There are many other threads on this topic which can be located by obvious searches. – Bill Dubuque Mar 15 '24 at 19:08