1. The problem statement, all variables and given/known data Prove that if 3|2a, then 3|a. 2. Relevant equations 3. The attempt at a solution I'm pretty sure that I proved it. Although, I feel like something is wrong. Can you check it? Proof: Assume 3|a, so, by definition, 2a=3q for some q in the integers. And assume 3|a, then a=3p for some p in the integers. Subtracting the second equation from the first equation, we get 2a-a=3q-3p. Simplifying, we get a = 3(q-p). Since q-p is an integer, then 3|a. QED As a side note, i chose to assume the consequent because its kind of like when u have the equation x+2=0 and u plug in -2 to see what the answer is..because tehres only 2 options at that point, either x=-2 or x=/=-2 and x=/=-2 shows for an infinite poissbilities of points to check to show a contradiction so I chose instead to assume the one point and show its true.