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+nβmnm+n(1βm)nβ=0=0=mβ1mββ
for mξ =1. There are no solutions for which m=1. The solutions (m,mβ1mβ) are pairs of integers only if m is 0 or 2 .