Fibonacci sequence
posted by Mathslover .
The Fibonacci sequence
a1=1,a2=1,a3=2,a4=3,a5=5,a6=8…
is defined recursively using the formulas a1=a2=1 and an+2=an+an+1 for all n≥1. Find the greatest common divisor of a484 and a2013.

Fibonacci sequence 
Steve
It has been proven that
gcd(F_{m},F_{n}) = F_{gcd(m,n)}
So,
gcd(F_{484},F_{2013}) = F_{gcd(484,2013)} = F_{11 = 89}
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