Calculate GCD(Fib(531185354674),Fib(613570636967))

Question

I picked this problem from here http://mathalon.in/?page=show_problem.php&pid=106 . I don't know how to solve it accurately. The number seems too to be done by any computation method.

score 4 · Answer 1 · answered Jan 24 '11 at 11:14

4

GCD(Fib(531185354674),Fib(613570636967)) = Fib(GCD(531185354674,613570636967))

answered Jan 24 '11 at 11:14

lhf

Yes, and $\text{GCD}(531185354674, 613570636967)=67$ and $\text{Fib}_{67}=44945570212853$ – Listing Jan 24 '11 at 13:20

score 3 · Accepted Answer · answered Jan 24 '11 at 11:13

Try and compute $\gcd(F_i,F_j)$ for some small $i$ and $j$ and see if you can spot a pattern.

Using the following three facts you can prove by induction that the pattern holds in general:

2 Answers2