<s>[INST] When $Z$ is divided by $8$ the remainder is $5$. When $Z$ is divided by $8$ the remainder is $5$. What is the remainder when $4Z$ is divided by $8$?
My Attempt:
We know,
$$\textrm{dividend} =\textrm{divisor} \times \textrm{quotient} + \textrm{remainder}$$
$$Z=8\times k+5$$
$$Z-5=8K$$
$$\dfrac {Z-5}{8}=k$$
Now, what should I do further?
 [/INST] $$\begin{align}Z&=8k+5\to \\4Z&=4(8k)+4\cdot 5\\&=8(4k)+20\\
&=8(4k)+16+4\\&=8(4k+2)+4\end{align}$$
So the remainder is $4$.
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