2 A sequence \(\left\{ u _ { n } \right\}\) is given by \(u _ { n + 1 } = 4 u _ { n } + 1\) for \(n \geqslant 1\) and \(u _ { 1 } = 3\).
- Find the values of \(u _ { 2 } , u _ { 3 }\) and \(u _ { 4 }\).
- Solve the recurrence system (*).
- Prove by induction that each term of the sequence can be written in the form \(( 10 m + 3 )\) where \(m\) is an integer.
- Show that no term of the sequence is a square number.