On the divisibility of binomial coefficients
Abstract
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 (n choose k) 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.
Keywords
Binomial coefficients, divisibility, primorials
DOI: https://doi.org/10.26493/1855-3974.2103.e84
ISSN: 1855-3974
Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications