This article focuses on the handling of signed numbers in order to trace mutual influences among Chinese, Japanese, and Korean mathematicians in the 17th and 18th centuries. \par The {\it Jiuzhang suanshu} (Arithmetic in nine chapters, probably 1st century CE), in a chapter on solving systems of linear equations using `square arrays' ({\it fangcheng}), gives the easily memorized {\it Zhengfu shu} (Rule for positive, {\it zheng,} and negative, {\it fu}), for adding and subtracting signed numbers. Translating according to the author's interpretation, the rule is as follows: \par When subtracting a number, \roster \item" " If it has the same sign, subtract. \item " " If it has the opposite sign, add. \item " " If it is positive and has no counterpart ({\it ren}), make it negative. \item " " If it is negative and has no counterpart, make it positive. \item " " If $a>b>0$, \item " " $(\pm a)-(\pm b)=\pm(a-b)$; \item " " $(\mp a)-(\pm b)=\mp(a+b)$; \item " " $0-(+a)=-a$; \item " " $0-(-a)=+a$. \endroster \par When adding a number, \roster \item " " If it has the opposite sign, subtract. \item " " If it has the same sign, add. \item " " If it is positive and has no counterpart, make it positive. \item " " If it is negative and has no counterpart, make it negative. \item " " $(\pm a)+(\mp b)=\pm(a-b)$; \item " " $(\pm a)+(\pm b)=\pm(a+b)$; \item " " $0+(+a)=+a$; \item " " $0+(-a)=-a$. \endroster (The English translation is the reviewer's; the translation into modern notation is the author's. Note the author's typographical error in the last line.) \par The word {\it ren} (Unicode U+4EBA), here translated `counterpart' following a gloss by Liu Hui (3rd cent. CE), normally means `person', and its use here is odd. It may be a scribal error for some other character, but the mathematical sense is clear, and the passage has always been understood as shown here. \par Yang Hui in his {\it Xiangjie Jiuzhang suanfa} (Detailed explanations of the Jiuzhang suanshu, 1261) emends this {\it ren} to the very similar character {\it ru} (Unicode U+5165), `enter', and presumably, e.g., the fourth line of the translation above should read, `If it is positive, and there is nothing to enter it into, make it negative', though this stretches the grammar a bit. Most modern editions of the {\it Jiuzhang suanshu} accept this emendation. \par A generation later, Zhu Shijie in his {\it Suanxue qimeng} (Introduction to mathematics, 1299) quotes the {\it Zhengfu shu} and states, `substituting {\it ru} for {\it ren} is incorrect'. \par The Korean mathematician Hwang Yun-sok (1729--1791) in his {\it Sanhak ibmun} (Introduction to mathematics, 1744) states a version of the {\it Zhengfu shu} and follows Zhu Shijie in using the word {\it ren}. \par The Japanese mathematician Takebe Katahiro (1664--1739) in his {\it Sangaku keimo genkai taisei} (Detailed explanations of {\it Suanxue qimeng}, 1690) states a version of the {\it Zhengfu shu}, but uses a zero symbol (a circle), avoiding the choice between {\it ren} and {\it ru}. Details in his handling of signed numbers in the `square arrays' technique and in the numerical solutions of polynomials (the Ruffini-Horner method) indicate that he has a developed concept of negative numbers that Hwang Yun-sok lacked. The author compares this to work by Li Shanlan (1810--1882), who was familiar with Western mathematics. \par Appendix I gives the detailed working for one of the `square array' problems in {\it Suanxue qimeng}. Appendix 2 gives the text of a treatment of {\it Zhengfu shu} by Li Shanlan. \par