Hint: Play with the Binomial on the right...
My question is simple: how do I proof that 9 | binomial(2^(k+1),2^k), where k >= 3 integer?
I have an idea: from 1 to 2^k there are n numbers that divisible by 9, from 2^k+1 to 2^(k+1) there are n+1 numbers that divisible by 9.
Is that the correct way to proof?
Thanks in advance!