This question was originally posted on: cstheory.stackexchange
Given $xyz=C$ where $x, y,$ and $z$ are integer variables and $C$ is integer constant. Assume all integers are encoded in binary.
What is the complexity of finding $x, y, z$ such that $xy+xz+yz$ has minimum value? Is there any subexponential algorithm that solves this problem? Does the problem become easier when integers are encoded in unary?
Motivation: I'm interested in the following generalized problem:
Input: integers $C$ and $K$
Problem: Find integers $x$, $y$, and $z$ such that $xyz\ge C$ and $xy+xz+yz\le K$