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

 

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

 

laugh

 Aug 5, 2021

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