2019/06/16 by Casacuberta, Sílvia
#11B65 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1906.07652
In Pacific J. Math. 292 (2018), 223-238, Shareshian and Woodroofe asked if for every positive integer n there exist primes p and q such that, for all integers k with 1 ≤ k ≤ n-1, the binomial coefficient \binomnk is divisible by at least one of p or q. We give conditions under which a number n has this property and discuss a variant of this problem involving more than two primes. We prove that every positive integer n has infinitely many multiples with this property.