6 The Fibonacci sequence \(\left\{ F _ { n } \right\}\) is defined by \(F _ { 0 } = 0 , F _ { 1 } = 1\) and \(F _ { n } = F _ { n - 1 } + F _ { n - 2 }\) for all \(n \geqslant 2\).
- Show that \(F _ { n + 5 } = 5 F _ { n + 1 } + 3 F _ { n }\)
- Prove that \(F _ { n }\) is a multiple of 5 when \(n\) is a multiple of 5 .