- (i) A sequence of numbers is defined by
$$\begin{gathered}
u _ { 1 } = 5 \quad u _ { 2 } = 13
u _ { n + 2 } = 5 u _ { n + 1 } - 6 u _ { n } \quad n \geqslant 1
\end{gathered}$$
Prove by induction that, for \(n \in \mathbb { Z } ^ { + }\),
$$u _ { n } = 2 ^ { n } + 3 ^ { n }$$
(ii) Prove by induction that for \(n \geqslant 2\), where \(n \in \mathbb { Z }\),
$$f ( n ) = 7 ^ { 2 n } - 48 n - 1$$
is divisible by 2304
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