This mathematical problem was first put forward and described by the title "I don't know how many counts there are" in Sun Tzu's The Art of War. The topic of "unknown things" is like this:

"I don't know the number of some things today. If you count in twos and threes, there are two left in the end; Five times five, and finally there are three left; If you multiply by seven, there are two left in the end. Q: How many of these things are there? "

It's not what you understand. Actually, 70 is divisible by 5 and 7 but divisible by 3 1, 2 1 divisible by 3 and 7 but divisible by 5/,1 5 divisible by 3 and 5 but divisible by 7/. In the title, if this number is divided by 3, then 70 times 2, 3 times 5, then 2 1 times 3, 2 times 7, and then 15 times 2 and adds up. 70×2

+

2 1×3

+ 15×2=233。

Subtract multiples of the least common multiple of 3, 5 and 7 as appropriate. Subtract 105 from this question twice to get 23.

This system algorithm was put forward by Qin, a mathematician in the Southern Song Dynasty.

This is the famous China remainder theorem.