numbers problem

For reals, x = y = sqrt(z)
For integers, this is as hard as a primality test.

I'm assuming that you want integer solutions, since otherwise it's fairly trivial as x = y = sqrt(z).

At a guess, I'd say you could simply start at floor(sqrt(z)) and march down until you find a factor, which then gives you y as z/x. I don't know if that's an optimal solution. Probably not.

Hmm I figured this would be problematic. I may just have to find another approach, funny how presumably small things can limit you :)

What do you need this for?

I assume you are using the computer integer datatype so the set of all possible numbers you may choose has a maximal element. You need not abandon that method if you are only going to be choosing from a subset of said set. Say if size of this subset is sufficiently small, |N| < 10^12? With M, the maximal, increasing with relaxing of time constraints.

There are a number of options including use of factorisation algorithims or sorted table of lists of factors.

Interesting.
The sorted table seems like a viable option.

Thanks.