# Should I really compute that monster?

Number Theory Level 3

Let $$F_n$$ denote the $$n^\text{th}$$ Fibonacci number.

Compute $$\gcd(F_{2000}F_{16} + F_{1999}F_{15}, F_{1014}F_{1001} + F_{1013}F_{1000})$$.

Notation: $$\gcd(a,b)$$ denotes greatest common divisor of $$a$$ and $$b$$.

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