$\forall n \in N; 7^{211} - 4^{2 n}$ is dlvisible by

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Solution

The correct option is B 3
Consider Option B,
$7 \equiv 1 (m o d 3)$
$4 \equiv 1 (m o d 3)$
Thus,
$7^{211} - 4^{2 n} \equiv 1^{211} - 1^{2 n} \equiv 1 - 1 \equiv 0 (m o d 3)$
Hence above expression is divisible by 3.

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