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# HELP!

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If $n \equiv 2 \pmod{7}$, then find the remainder when $(n + 2)(n + 4)(n + 6)$ is divided by 7.

Aug 4, 2021

#1
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If $$n \equiv 2 \pmod{7}$$,
then find the remainder when
$$(n + 2)(n + 4)(n + 6)$$ is divided by $$7$$.

$$\begin{array}{|rcll|} \hline \mathbf{(n + 2)(n + 4)(n + 6) \pmod{7}} &\equiv& (2 + 2)(2 + 4)(2 + 6) \pmod{7} \\ &\equiv& 4*6*8 \pmod{7} \\ &\equiv& 192 \pmod{7} \\ &\equiv& {\color{red}3} \pmod{7} \\ \hline \end{array}$$

Aug 5, 2021