Shareshian and Woodroofe asked if for every positive integer ?$n$? there exist primes ?$p$? and ?$q$? such that, for all integers ?$k$? with ?$1 \le k \le n-1$?, the binomial coefficient ?$\binom{n}{k}$? 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.

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URN

URN:NBN:SI:DOC-U7TDJLJG

COBISSID

44726019

Added

28.04.2021

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Citation

APA:

Casacuberta, Sílvia (2020). On the divisibility of binomial coefficients. Ars mathematica contemporanea, volume 19, issue 2, str. 297-309. URN:NBN:SI:DOC-U7TDJLJG from http://www.dlib.si

MLA:

Casacuberta, Sílvia. "On the divisibility of binomial coefficients." Ars mathematica contemporanea volume 19. issue 2 (2020) str. 297-309.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-U7TDJLJG>

Ars mathematica contemporanea
2008-
(Assembly record)