I am working with the equation: $ab+bc+ac-a-b-c=100$. I need to find all integer solutions for this. What I figure out for now is that I can turn it into $(a-1)(b-1)(c-1)=abc-101$. But this does not help me to go further.
My questions are : how to find all integer solutions. and is there a general category of this kind of questions? for example, finding integer solutions of linear equation system that the number of unknown is greater than the number of equations?