A unit fractionis a fraction of the form 1/n for some nonzero integer n. Compute the number of ways we can write 1/6 as the sum of two distinct positive unit fractions. (The order of the fractions in the sum does not matter, so 1/2+1/3 would be considered the same sum as 1/3+1/2)
+128408 1/a + 1/b = 1/6
a, b must be > 6
So.....let z = 6 a = z + m b = z + n
So we have
1/ ( z + m) + 1/ ( z + n) = 1 / z simplify
z [ 2z + m + n) = (z + m) (z + n)
2z^2 + zm + zn = z^2 + zm + zn + mn
z^2 = mn
6^2 = mn
36 = mn
m n a = z + m b = z + n
1 36 7 42
2 18 8 24
3 12 9 18
4 9 10 15
6 6 12 12 (reject this)
So...we can wirite 1/6 as the sum of four different pairs of unit fractions
