perplexus.info :: Numbers : GCD of Fibonacci 2

GCD of Fibonacci 2 (Posted on 2016-03-23)

This is an extension of GCD of Fibonacci.

Denote the nth term of the Fibonacci sequence as F(n), with F(0)=0 and F(1)=1. Let S_n be the set {F(n), F(n+1), F(n+2), F(n+3)}.

For what values n does there exist a pair of numbers from S_n with a GCD greater than 1?

Submitted by Brian Smith

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Solution: (Hide)

For n=3k the GCD of F(n) and F(n+3) is 2. In all other cases the GCD of any pair is 1.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: possible solution	broll	2016-03-24 00:09:54
possible solution	armando	2016-03-23 09:53:30

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