Hello, First I will post the question that I am working on. I am not good at proofs (even elementry proofs such as these ones). I was wondering if someone could take a look at my work and perhaps confirm whether my proofs are adequate and/or make some suggestions. First I will start off with a basic definition of a divisor: An integer, a, not equal to zero, is called a divisor of an integer b if there exists an integer c such the b = a c. i) If a|b then -a|b. Assume a|b. Then b = a c for some integer c by def. Let c = -k where -1, k are integers. Then b = a (-k) = - a k. Since k is an integer, then by def., if a|b then b = -a k. Similarly, ii) If a|b then a|-b. Assume a|b. Then b = a c for some integer c by def. Let c = -k where -1, k are integers. Then b = a c = a -k = -a k = -(a k) -b = --(a k) -b = a k Once again since k is an integer, then by def., if a|b then -b = a k. Also iii) If a|b then -a|-b. I am sort of stuck on this one. I am not yet sure how to show If a|b then -a|-b. I thought b = a c, -b = -a c By definition, -a|-b if -b = -a c for some integer c. Since c is an integer, then by def. if a|b then -a|-b. Part iii) seems pretty weak to me. In fact all look pretty weak now. Any help/insights are appreciated. Thankyou.