# Chinese Remainder Theorem : Problem of Sun-Tsu

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Find all solutions of the problem of Sun-Tsu. Find all integers x such that the remainder after division by 3 is equal to 2, the remainder after division by 5 is equal to 3, the remainder after division by 7 is equal to 2.

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#### Solution Preview

Solution

From the question, we can get three equations as follow:

x = 2 (mod 3)

x = 3 (mod 5)

x = 2 (mod 7)

From the first equation, we got x = 3t + ...

#### Solution Summary

The problem of Sun-Tsu is solved and explained. The Chinese remainder theorem for Sun-Tsu is provided.

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