Question

Show that 3 · 4n + 51 is divisible by 3 and 9 for all positive integers n.
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Answer 1

4^1 + 17 = 21 , which is divisible by 3. 4^k + 17 and 3 * 4^k are both divisible by 3, so 4^k + 17 + 3 * 4^k is divisible by 3 as well. 3 * (4^n + 17) would be divisible by 9