$31 \cdot 17$ The number of integer pairs $(m, n)$ that satisfy the equation $m+n=mn$ is
(A) 1 .
(B) 2 .
(C) 3 .
(D) 4 .
(E) greater than 4.
(28th American High School Mathematics Examination, 1977)
[Solution] If $m+n=mn$, then $m+n-mn=0$, i.e., $\square$ we get
$$
\begin{array}{l}
m+n(1-m)=0, \\
n=\frac{m}{m-1} \quad(m \neq 1) .
\end{array}
$$

When $m=1$, there is no solution; only when $m=0$ or 2, the solution $\left[m, \frac{m}{m-1}\right]$ is an integer pair, i.e., there are two solutions $(0,0)$ and $(2,2)$.
Therefore, the answer is $(B)$.