Recent content by riemann75024

Re: ??Divisibility of Binomial Coefficients?? But I'm not looking to see if n is divisible by $\displaystyle\binom{n}{k}$, but rather if $\displaystyle\binom{n}{k}$ is divisible by n when n is prime for each k, because $\displaystyle\binom{n}{k}$ is not divisible by n for each k when n is not...

Re: ??Divisibility of Binomial Coefficients?? Ok I see that now, thank you! But one more question then, when the "n" in my original example is a prime number does that make a difference, ignoring the first and last coefficients? In other words, if you take an example of n being non-prime...

Re: ??Divisibility of Binomial Coefficients?? I see the k=0 case, but the k=n case is not immediately clear to me. Do you mean that when k=n one of the terms in the numerator is 0, and thus we have something like 0/k!? Sorry if I am missing something painfully obvious or basic…

Hi all, I am trying to figure out if there is a pre-existing theorem and proof of whether or not each of the binomial coefficients in a binomial expansion of (a +b)^n are divisible by n, particularly in the case where n is a prime number. Has this already been asked and answered somewhere in...