Find the number of ordered pairs (m,n) of integers that satisfy \(mn = 2m + 4n. \)
mn = 2m + 4n rearrange as
mn - 4n = 2m
n ( m - 4) = 2m
n = 2m / [ m - 4 ]
When
m n
0 0
3 -6
5 10
6 6
8 4
12 3
2 -2
-4 1
So it's 8? Tysm!
Another way:
Rearrange the equation mn=2m+4n as mn-2m-4n=0
Notice that this equation is close to (m-4) * (n-2) is eight is added to both sides.
(m-4) * (n-2) = 8
8=2^3, so four factors.
2(4)=8-total ordered pairs(negative and non-negative)......
Thx, tertre !!!!
+129899 
