I took a quick stab at it. I'm not done, but heres a strategy I was working on.
First, find the maximum value for x (by minimizing y) and then a max value for y (by minimizing x)
to find the max value of x, write a loop that breaks when a solution is found, set y and x to 1, and increase x until the result is greater then c, then increment y and repeat (hope thats understandable)
To find all solutions, then, you could just bruteforce it and try every combination of numbers less then max x and max y. Theres certainly cleverer ways to do it, thats just as far as i've gotten so far and I have to go to class now
good luck, hope that hint helps.