Greatest Common Divisor with Fibonacci Numbers

Question

Prove that for all integers $n\geq 0$:

$$\gcd(F_{n+1},F_n)=1$$

I am extremely lost. Please can some provide some hint or direction? Thank you so very much

See http://math.stackexchange.com/questions/24378/prove-that-two-any-consecutive-terms-of-fibonacci-sequence-are-relatively-prime — lab bhattacharjee, Feb 24 '16 at 06:07

score 6 · Accepted Answer · answered Feb 24 '16 at 05:58

6

The Euclidean algorithm, $\gcd(a,b)=\gcd(a-b,b)$ works well with the Fibonacci recurrence.

answered Feb 24 '16 at 05:58

Ross Millikan

1 Answers1