prove that if d divides n then prove that
fibonacci of d divides fibonacci of n.
i have tried to write F(n) as a multiple of F(d) using the fact that n=ad for some natural a but got nowhere..
Answer
By the addition law f(x+y)=if(x)+jf(y) for i,j∈Z, so by induction f(d)∣f(nd)
f((n+1)d)=f(nd+d)=if(nd)+jf(d)=ikf(d)+jf(d)=(ik+j)f(d)
Remark More generally gcd For a proof see here.
No comments:
Post a Comment