8 Let \(f ( n )\) denote the base- \(n\) number \(2121 _ { n }\) where \(n \geqslant 3\).
- For each \(n \geqslant 3\), show that \(\mathrm { f } ( n )\) can be written as the product of two positive integers greater than \(1 , \mathrm { a } ( n )\) and \(\mathrm { b } ( n )\), each of which is a function of \(n\).
- Deduce that \(\mathrm { f } ( n )\) is always composite.
- Let \(h\) be the highest common factor of \(\mathrm { a } ( n )\) and \(\mathrm { b } ( n )\).
- Prove that \(h\) is either 1 or 5 .
- Find a value of \(n\) for which \(h = 5\).