The Greatest Common Divisor of Sets of Binomial Coefficients with Restrictions

Abstract

Ram (1909) proved an elegant result for the greatest common divisor of a set of binomial coefficients, and many researchers have proved similar results along these lines. In this paper, we will turn to the results of the greatestcommon divisor of sets of binomial coefficients with  restrictions. Specifically, we give the answer to gcdA2(n) for several cases depending on the value of s = σ_p(n) where p | n−1. (Notations will be introduced below.) We raise some open questions and conjectures for the interested readers to pursuit.