Chapter 44 Section Two

The equation chapter of "Nine Chapters of Arithmetic" has a question about five common wells: "Today, there are five common wells. If A and two are not enough, such as B and one; B and three are not enough, and C is one; If Ding and Wufu are not enough, use Wu and one rice; if Wu and Liu are not enough, use Jia and one. If each of them gets less than one rice, they will all be arrested. Ask the geometry of the depth of the well and the length of the rope?” According to the art, the equation listed is: "Nine Chapters" is solved according to the equation, and it is obtained that x=265, y=191, z=148, u=129, υ=76, w=721.There are six unknowns in this question, and only 5 lines of equations can be listed. The result of element elimination should be υ=76/721w.Liu Hui pointed out that the solution of "Nine Chapters" is "expressed in words", and in fact only the smallest set of positive integer solutions is given.This is an indeterminate problem, and it is the first time in the history of Chinese mathematics that an indeterminate problem has been explicitly raised.