Prime power divisors of binomial coefficients

P. Erdős, Grigori Kolesnik

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

It is known that for sufficiently large n and m and any r the binomial coefficient (Formula Presented) which is close to the middle coefficient is divisible by pr where p is a 'large' prime. We prove the exact divisibility of (Formula Presented) by pr for p>c(n). The lower bound is essentially the best possible. We also prove some other results on divisibility of binomial coefficients.

Original languageEnglish
Pages (from-to)101-117
Number of pages17
JournalDiscrete Mathematics
Volume200
Issue number1-3
Publication statusPublished - Apr 6 1999

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Binomial coefficient
Divisibility
Divisor
Divisible
Lower bound
Coefficient

Keywords

  • Divisibility of binomial coefficients

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Prime power divisors of binomial coefficients. / Erdős, P.; Kolesnik, Grigori.

In: Discrete Mathematics, Vol. 200, No. 1-3, 06.04.1999, p. 101-117.

Research output: Contribution to journalArticle

Erdős, P & Kolesnik, G 1999, 'Prime power divisors of binomial coefficients', Discrete Mathematics, vol. 200, no. 1-3, pp. 101-117.
Erdős, P. ; Kolesnik, Grigori. / Prime power divisors of binomial coefficients. In: Discrete Mathematics. 1999 ; Vol. 200, No. 1-3. pp. 101-117.
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