Geodesic
On the divisibility of binomial coefficients
Ars Mathematica Contemporanea, Tome 19 (2020) no. 2, pp. 297-309.

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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.
DOI : 10.26493/1855-3974.2103.e84
Keywords: Binomial coefficients, divisibility, primorials 
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Sílvia Casacuberta. On the divisibility of binomial coefficients. Ars Mathematica Contemporanea, Tome 19 (2020) no. 2, pp. 297-309. doi : 10.26493/1855-3974.2103.e84. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2103.e84/

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