$7^{n + 1} + 3^{n + 1}$ is divisible by

10

for all natural numbers n

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10

for odd natural numbers n

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10

for even natural numbers n

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None of these

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Solution

The correct option is C $10$ for even natural numbers n
Given that,

$7^{n + 1} + 3^{n + 1}$

We know that, $a^{n} + b^{n}$ is divisible by $(a + b)$ for even natural number n.

Hence, $7^{n + 1} + 3^{n + 1}$ is divisible by $(7 + 3) = 10$ for even natural number n.

Hence, this is the answer.

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