Prove that for all natural numbers statement n, statement is dividable by 7
$$15^n+6$$
Base. We prove the statement for $n = 1$
15 + 6 = 21 it is true
Inductive step.
Induction Hypothesis. We assume the result holds for $k$. That is, we assume that
$15^k+6$
is divisible by 7
To prove: We need to show that the result holds for $k+1$, that is, that
$15^{k+1}+6=15^k\cdot 15+6$
and I don't know what to do
Answer
Observe that $14$ is divisible by 7. Then let $15^k\cdot 15+6=15^k\cdot 14+ 15^k+6$.
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