Problem: How many pairs ( m,n ) of integers satisfy the equation m+n=mn?
Answer Choices:
A. 1
B. 2
C. 3
D. 4
E. more than 4
Solution:
If m+n=mn, then
m+n−mnm+n(1−m)n​=0=0=m−1m​​
for mî€ =1. There are no solutions for which m=1. The solutions (m,m−1m​) are pairs of integers only if m is 0 or 2 .