4 The expression \(\mathrm { f } ( n )\) is given by \(\mathrm { f } ( n ) = 2 ^ { 4 n + 3 } + 3 ^ { 3 n + 1 }\).
- Show that \(\mathrm { f } ( k + 1 ) - 16 \mathrm { f } ( k )\) can be expressed in the form \(A \times 3 ^ { 3 k }\), where \(A\) is an integer.
- Prove by induction that \(\mathrm { f } ( n )\) is a multiple of 11 for all integers \(n \geqslant 1\).