# 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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