I have a function $f(m,n)$ where m and n are positive integers. Suppose $f(m,n)$ is like a black box, I can get values of it when I enter values of m and n. I want to scan over a region for example $4<m<100, 4<n<1000$ to find where $f(m,n)<0$. Then make a plot of the region where it satisfies the requirement.
For the plot part, I think I can directly use the Listplot if I can successfully generate a parameter list for m and n where $f(m,n)<0$. For the first part, I could use the command For to generate the list satisfying the requirement. I guess this is not the most ideal command I want to use in Mathematica.