- (i) Prove by induction that for \(n \in \mathbb { Z } ^ { + }\)
$$\left( \begin{array} { l l }
5 & - 8
2 & - 3
\end{array} \right) ^ { n } = \left( \begin{array} { c c }
4 n + 1 & - 8 n
2 n & 1 - 4 n
\end{array} \right)$$
(ii) Prove by induction that for \(n \in \mathbb { Z } ^ { + }\)
$$f ( n ) = 4 ^ { n + 1 } + 5 ^ { 2 n - 1 }$$
is divisible by 21
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