Let 

First prove that there is at least one
value of n for which  is divisible by 21:








Strategy:
If n=k is a value of n so that f(n=k) is divisible by 21,
then if f(k+1) and f(k) differ by a multiple of 21, then 
f(k+1) will also be divisible by 21.

So, we will consider the difference f(k+1)-f(k)  

But first we must calculate f(n=k+1):






Now we consider 



And since we know that since f(1) is divisible by 21
then f(2) is also divisible by 21, and thus f(3) is
also divisible by 21, etc., etc.

Edwin