Sun Tzu’s Chinese Remainder Theorem

Around 300 BC, the following problem was posed in the ancient Chinese book Sun-tzu Suan-ching: “There are certain things whose number is unknown. If we count them by threes, we have two left over; by fives, we have three left over; and by sevens, two are left over. How many things are there?” We solve this concrete problem and describe the general theorem, which is called the Chinese Remainder Theorem (CRT). We also describe an even more general theorem where the moduli are not necessarily pairwise coprime, which is a result that is rarely mentioned in the literature.

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