Fibonacci Numbers
Number Theory
Level
1
What is the greatest common divisor of the 2013th and 2014th Fibonacci Number?
The answer is 1.
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It all comes down to the fact that g c d ( a , b ) = g c d ( a + b , b ) .
Since g c d ( f 1 , f 2 ) = 1 , it would be the same all the other consecutive Fibonacci number pairs.