Hey all I would really love some help with this fibonacci proposition:
For all k,m in the Natural Numbers, fib(mk) is divisible by fib(m)
Thanks a bunch!
I think the original problem can be solved using the identity
$\displaystyle F_{m+n} = F_{m-1}F_n + F_mF_{n+1}$
which holds for all positive integers m,n. This identity can be proved by fixing m, say, and inducting on n. Then, prove that
$\displaystyle F_m$ divides $\displaystyle F_{mk}$
with another inductive argument, using the above identity.