You know this!

Number Theory Level 2

True or False?

Successive terms of the Fibonacci sequence have a greatest common divisor of 1.

False True

Ekene Franklin by EKENE FRANKLIN , 16, Nigeria

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Michael Mendrin
Sep 7, 2018

If F n − 2 + F n − 1 = F n F_{n-2}+F_{n-1}=F_n and if F n − 1 F_{n-1} and F n F_n have a prime factor p p in common, then F n − 2 F_{n-2} would also. Then all of the Fibonacci numbers would have this prime factor p p , which is an impossibility.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Winston Choo
Sep 7, 2018

Well, each successive terms of the Fibonacci sequence has a ratio that gets closer and closer to 1.618.... (The Golden Ratio). So there is obviously no gcd of more than 1.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...