Consider the Fibonacci numbers

MATHEMATICS · Subjective · A Level · Mathematics · Proof · Proof

Problem

Consider the Fibonacci numbers. Let

f_1 = 1, f_2 = 1

and

f_n = f_{n-1} + f_{n-2}

for

n > 2

. Prove that

\gcd(f_m, f_n) = f_{\gcd(m,n)}