Solving equations with "mod" 1. The problem statement, all variables and given/known data I have a homework problem. I'm in computer science, however one of my programs requires me to solve this equation. I'm afraid it's beyond my expertise. (a * x) mod b = 1 This needs to be rearranged in the form of x = ... Due to the existence of "mod", I get confused. Please don't solve it for me. I'm just looking for a little nudge to help me get over this hump. 2. Relevant equations See above. 3. The attempt at a solution My main goal solving this was to try and get rid of that "mod". Thinking about it logically, if x mod y = 0, that means that x / y = Z, where Z is some integer. I also believe it means there exist values of x and y such that all integer values of Z would exist. Base equation (a * x) mod b = 1 Subtracting 1 from both sides ((a * x) - 1) mod b = 0 Converting to division ((a * x) - 1) / b = Z Solve like normal x = (Z*b + 1) / a Now the problem is, the Z is throwing me off. Do I just choose a value? It would make sense for remainders that there are multiple values of x that keep the equation in balance. Due to this being programming, x can be my only unknown. Am I on the right track?