$7^{4 n} - 6^{4 n}$ , where n is an integer > 0, is divisible by?

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All of these

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Solution

The correct option is D All of these
$7^{4 n} - 6^{4 n}$
$7^{2^{2 n}} - 6^{2^{2 n}}$
$49^{2 n} - 36^{2 n}$
So, it must be divisible by (49 + 36) = 85 and (49 - 36) = 13
The expression given is divisible by $85 (17 \times 5)$ and 13

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