MathDB

2009 ToT Spring Junior A P7 common divisors of binomials

Source:

March 7, 2020

Binomialcombinatorics

Problem Statement

Let

{n \choose k}

be the number of ways that

k

objects can be chosen (regardless of order) from a set of

n

objects. Prove that if positive integers k and l are greater than

1

and less than

n

, then integers

{n \choose k}

and

{n \choose l}

have a common divisor greater than

1