4 Let \(\mathrm { N } = 10 \mathrm { a } + \mathrm { b }\) and \(\mathrm { M } = \mathrm { a } + 3 \mathrm {~b}\), where \(a\) and \(b\) are integers such that \(a \geqslant 1\) and \(0 \leqslant b \leqslant 9\).
- Prove that \(29 \mid N\) if and only if \(29 \mid M\).
- Use an iterative method based on the result of part (a) to show that 899364472 is a multiple of 29 .