Show that if a, b, c, and d are integers such that

a | c and b | d, then ab | cd.

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- Nov 5th 2009, 06:14 AMracewithferrariprovind mods in series, sequences, integers and functions
Show that if a, b, c, and d are integers such that

a | c and b | d, then ab | cd. - Nov 5th 2009, 08:42 AMDefunkt
From $\displaystyle a|c$ we get that for some $\displaystyle m \in \mathbb{N}$, c = am. Also, from $\displaystyle b|d$ we get that for some $\displaystyle n \in \mathbb{N}$, d = nb.

Now, what is ab? Can you see how the above facts help us show the desired result?