Two categories of indeterminate problem are commonly found in Chinese mathematics:
(i) Problems which translate into systems of linear equations of degree one of type:
(ii) Problems which reduce to systems of simultaneous congruences:
A problem of the first category is usually referred to as a "hundred fowls problem" even if its statement does not relate
to farmyard birds, since the oldest problem of this type is that found in the Zhang Qiujian suanjing (Zhang Qiujian's Computational Canon, end of the fifth century AD) which involves cockerels, hens and chickens.
As far as problems of the second category are concerned, these are usually referred to in modern books on number theory as
"remainder problems" (since they involve the following question: find a number which when divided by ml, m2, m3, ... , has remainders rl, r2, r3, ... , respectively). Moreover, the solution of these problems is said to depend upon the "Chinese remainder theorem." This
expression alludes to an algorithm which first appears in the Shushu jiuzhang (Computational Techniques in Nine Chapters, 1247) by Qin Jiushao.