Exercise 1.2.10 (Divisibility of products)

Question

Given $a\mid b$ and $c \mid d$, prove that $ac \mid bd$.

Richard Ganaye · Accepted Answer

ewcommand{\Z}{\mathbb{Z}}

\begin{proof} 
Assume that $a\mid b$ and $c \mid d$. There are integers $k,l$ such that $b = ka, d = lc$, thus $bd =(kl) ac$. Since $K = kl \in \Z$, and $bd = K (ac)$, we obtain $ac \mid bd$.

(Note that $a 
e 0$ and $c 
e 0$ imply $ac 
e 0$.)
\end{proof}

Exercise 1.2.10 (Divisibility of products)

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Exercise 1.2.10 (Divisibility of products)

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