Undernetmath’s Weblog

Solutions_2010


2010-12-6 number theory quickie by Stumbo

Let n, k be 2 positive integers with n\geq 2k.
Show that either \binom{n}{k} or \binom{n-k}{k} is divisble by 2.
Solution by Stumbo
The product of those binomial coefficients, divided by two, is the number of unordered disjoint pairs of K-subsets of an N-set. Thus the product of the coefficients is even, so at least one of them must be even.

Leave a Comment »

No comments yet.

RSS feed for comments on this post. TrackBack URI

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Blog at WordPress.com.

%d bloggers like this: