Binomial coefficients with divisors avoiding an interval

Hung M. Bui, Slava Naprienko, Kyle Pratt +1

We solve a fifty-year-old conjecture of Erdős and Graham concerning whether the binomial coefficient $\left(\genfrac{}{}{0ex}{}{n}{k}\right)$ with $1\le k\le \frac{n}{2}$ must always have a divisor $\…