How many distinct ordered pairs of positive integers (m,n) are there so that the sum of the reciprocals of m and n is 1/4?
Let z = 4
Let m = z + a
Let n = z + b
And we can find a, b such that
ab = z^2
ab = 4^2
ab = 16
The factors of 16 are
1 2 4 8 16
So
a b
1 16
2 8
4 4
m n
5 20 accept
6 12 accept
8 8 reject since m,n are distinct
