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  4. For all positive integral values of n, 32n - 2n +1 is divisible by

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Q. For all positive integral values of $n, 3^{2n} - 2n +1$ is divisible by

Principle of Mathematical Induction

Solution:

Putting $n = 2$ in $3^{2n} -2n + 1$ then,
$3^{2 \times 2} - 2 \times 2 +1 = 81- 4 +1 = 78$, which is divisible by $2.$