Integer combination i want write a module to find the integer combination for a multi variable fomula. For example
$8x + 9y \le 124$
The module will return all possible positive integer for $x$ and $y$.Eg. $x=2$, $y=12$.
It does not necessary be exactly $124$, could be any number less or equal to $124$. Must be as close as possible to $124$ if no exact solution could be found.
I do not want to solve with brute force as the number of variable could be any...$(5,10,100,...n)$
Any algorithm could solve this?

Considering the equal case, if you analyze some of the data points that produce integer solution to the original inequality:
$$...,(-34,44), (-25,36), (-16,28), (-7,20),(2,12),(11,4),...$$
you can see that:
$$x_{i}=x_{i-1}+9$$
to get $y$ values, re-write the inequality as follows (and use the equal part):
$$y = \frac{124-8x}{9}$$
using the above equations you can find $(x,y)$ values in a given range of $x$ values without brute force.
