## Fibonacci Multiples

The sequence \(1, 1, 2, 3, 5, \ldots\) is called the Fibonacci Sequence. It is the sequence \(f(1)\), \(f(2)\), \(f(3)\), \(f(4)\), \(\ldots\) defined by

- \(f(1) = 1\),
- \(f(2) = 1\), and
- \(f(n + 2) = f(n + 1) + f(n)\) for all \(n \ge 1\).

So for example \(f(12) = 144\).

Part A | Determine the smallest positive integer \(a\) such that \(F_a\) is a multiple of \(100\). | |
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Part B | Determine the smallest positive integer \(b\) such that \(F_b\) is a multiple of \(103\). | |

Part C | Determine the smallest positive integer \(c\) such that \(F_{c-1}\) is a multiple of \(100\) and \(F_{c+1}\) is a multiple of \(103\). |