So perhaps the complete answer of f(x) could be:
y = x * (x - n ) / n
where
n OR y is a divisor of x.
What do you think?
Kerim
Here is how you can find the complete solution:
you can rewrite 1/x + 1/y = 1/z as
(y+x)(x-z) = x^2
so the answers are related to the divisors of x^2. Also, as y>0 and z>0,
y+x > x and x-z < x, so this means we can start with divisors larger than √x^2 for (y+x).
As an example, for x = 6, if we look at all the divisors of 36, and associating (x+y) with the divisor:
you can see that only the divisors (x+y) > 6 have y > 0.
Restricting to divisors >6 for (x+y) gives;
which are all the solutions.
The number of solutions is the number of distinct divisors of x^2 which are greater than x.
So if x is prime you will only have one solution.
I'm not quite sure how 5th grade kids will cope!