Clearly I need to brush up on my number theory.. this was so much harder because the whole problem revolved around limiting solutions to integer values. Ultimately GCD was needed to make it an integer based solution, which I ultimately kinda knew, I knew I had to use GCD somewhere but took me a minute to realize where and put it into a final solution.... I feel like this took 10x longer than it would have a few years ago, just too long since i had to work with a GCD I guess or integer domain problems.