$\forall n \in N, 7^{2 n} - 48 n - 1$ divisible by

25

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26

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1234

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2304

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Solution

The correct option is D $2304$
Let $P (n) = 7^{2 n} - 48 n - 1$
$P (1) = 49 - 48 - 1 = 0 \Rightarrow P (1)$ is divisible by all $n \in N$
$P (2) = 7^{4} - 48.2 - 1 = 2304 \Rightarrow P (2)$ is divisible by $2304$
Hence option 'D' is correct choice.

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