Fibonacci

\[\large F_n = x! + y!\]

The above equation holds true for some positive integers \(n\), \(x\) and \(y\). Find the largest \(n<100\) satisfying this condition, and submit your answer as \(n+x+y\).

Notations:

  • \(F_n\) denote the \(n^\text{th} \) Fibonacci number, where \(F_0 = 0, F_1 = 1\) and \(F_n = F_{n-1} + F_{n-2} \) for \(n=2,3,4,\ldots \).

Notation: \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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