Thread: Divisibility of Binomial Coefficients

Hello!

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!

Hint: Play with the Binomial on the right...

I do not understand what you exactly think. Can you explain?

Originally Posted by Ben92

I do not understand what you exactly think. Can you explain?

Expand the binomial coefficient into its factorial form. I think induction works better but I have not tried it.