8. Prove by induction that, for \(n \in \mathbb { Z } ^ { + }\),
- \(\mathrm { f } ( n ) = 5 ^ { n } + 8 n + 3\) is divisible by 4 ,
- \(\left( \begin{array} { l l } 3 & - 2
2 & - 1 \end{array} \right) ^ { n } = \left( \begin{array} { l r } 2 n + 1 & - 2 n
2 n & 1 - 2 n \end{array} \right)\)