1. The problem statement, all variables and given/known data I reduced a much harder problem to the following: Prove that if abs(a-b) is divisible by k, and if abs(b-c) is divisible by k, then abs(a-c) is divisible by k. 2. Relevant equations none really. 3. The attempt at a solution I tried setting abs(a-b)/k = n and abs(b-c)/k = m where m and n are integers and trying to construct abs(a-c) from that but to no avail. By the definition of absolute value, I know abs(x) = x when x>0 and =-x when x<0. I think trying all of the four possible cases might work, but would there be an easier way?