中师部编教材《代数与初等函数》第二册第八章第三节中的定理3是这样叙述的:“设不定方程αx+by=c(α>0,b>0)有一个整数解x_0,y_0,则它的全部整数解可以表示成 x=x_0+bt y=y_0-αt其中t为任何整数。”我认为这一定理中关于解的一般形式值得商榷,按定理给出的解的一般形式,对有些不定方程漏掉了许多解。如:解不定方程4x+6y=10,因为x=1,y=1是这个方程的一个整数解,直接应用定理,得它的全部整数解集为A={(x,y):x=1+6t,y=1-4t,t∈z}。另一方面方程4x+6y=10又等价于2x+3y=5,这样, The division 3 textbook “algebra and elementary functions,” Volume II, Chapter VIII of the third section of Theorem 3 is described as follows: “Let the indefinite equation αx + by = c (α> 0, b> 0) has an integer Solution x_0, y_0, then its entire integer solution can be expressed as x = x_0 + bt y = y_0 - αt where t is any integer. ”I think the general form of this theorem about the solution is questionable, given by the theorem The general form of solution, many solutions to some indefinite equation omitted. Such as: Uncertain equation 4x + 6y = 10, because x = 1, y = 1 is an integer solution of this equation, the direct application of the theorem, it has all the integer solution set A = {(x, y): x = 1 + 6t, y = 1-4t, t∈z}. On the other hand, the equation 4x + 6y = 10 is again equivalent to 2x + 3y = 5,