Problem

Source: II International Festival of Young Mathematicians Sozopol 2011, Theme for 10-12 grade

Tags: number theory



Let $n$, $i$, and $j$ be integers, for which $0<i<j<n$. Is it always true that the binomial coefficients $\binom{n}{i}$ and $\binom{n}{j}$ have a common divisor greater than 1?