1. The problem statement, all variables and given/known data If a^2 divides b^2, then a divides b Also If a^2 divides b^3, then a divides b 2. Relevant equations 3. The attempt at a solution For the first question, if a^2 divides b^2, then b^2=(a^2)c where c is some integer c=(b^2)/(a^2) c=(b/a)^2 The answers in the back say that it is enough to show that c is a perfect square, but I don't see how that's sufficient. If c is a perfect square, then c is an integer, which implies that a^2 divides b^2, which we already knew. No idea where to go for the second question. The same strategy doesn't seem to work.