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Using Mathematical Induction Prove that $$3^{2n} + 7$$ is divisible by 8, $$\forall n \in \mathbb{N}$$.
Correct Answer: 0
PLACEHOLDER ANSWER - this is a proof question. For $$n = 1$$, $$3^2 + 7 = 16$$ is divisible by 8. If $$3^{2k} + 7 = 8m$$, then $$3^{2k + 2} + 7 = 9 \times 3^{2k} + 7 = 9(8m - 7) + 7 = 72m - 56 = 8(9m - 7)$$, which is divisible by 8. By induction, $$3^{2n} + 7$$ is divisible by 8 for all natural $$n$$.
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