A characterization of a prime $p$ from the binomial coefficient ${n \choose p}$

Alexandre Laugier, Manjil Saikia

Published 2012-09-07, updated 2014-05-01Version 4

We complete a proof of a theorem that was inspired by an Indian Olympiad problem, which gives an interesting characterization of a prime number $p$ with respect to the binomial coefficients ${n\choose p}$. We also derive a related result which generalizes the theorem in one direction.