# 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.

1. Steve

It has been proven that

gcd(Fm,Fn) = Fgcd(m,n)

So,

gcd(F484,F2013) = Fgcd(484,2013) = F11 = 89

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