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Inequality

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Question

Show that $2^{3 n} - 1$ , is divisible by $7$ .

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Solution

$2^{3 n} - 1$ divisible by 7
$(2^{3})^{n} - 1$
$8^{n} - 1^{n}$
$(8 - 1) (8^{n - 1}$ +- - - +1)
= 7 $\times$ Some Integer.
$∴$ It is divisible by 7.

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