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..

1. 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.