A characterization of a prime $p$ from the binomial coefficient ${n   \choose p}$
  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. 
Alexandre Laugier, Manjil Saikia
math.NT