5 For integers \(a\) and \(b\), with \(a \geqslant 0\) and \(0 \leqslant b \leqslant 99\), the numbers \(M\) and \(N\) are such that
$$M = 100 a + b \text { and } N = a - 9 b .$$
- By considering the number \(M + 2 N\), show that \(17 \mid M\) if and only if \(17 \mid N\).
- Demonstrate step-by-step how an algorithm based on the result of part (i) can be used to show that 2058376813901 is a multiple of 17 .