2010-12-6 number theory quickie by Stumbo

Let be 2 positive integers with .

Show that either or 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.

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