Division: Show that if a,b,c, and d are integers such thata|c and b|d, then ab|cd Solution We are given a|c, b|d. Thus, c = an and b = dm for some integers n and m. This means that cd = (an)(bm) = ab(nm). Since n and m are integers, nm is an integer. Thus, cd = abk, where k is the integer nm. Thus, ab|cd..