### 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 p^{r} where p is a 'large' prime. We prove the exact divisibility of (Formula Presented) by p^{r} for p>c(n). The lower bound is essentially the best possible. We also prove some other results on divisibility of binomial coefficients.

Original language | English |
---|---|

Pages (from-to) | 101-117 |

Number of pages | 17 |

Journal | Discrete Mathematics |

Volume | 200 |

Issue number | 1-3 |

Publication status | Published - Apr 6 1999 |

### Fingerprint

### Keywords

- Divisibility of binomial coefficients

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*200*(1-3), 101-117.

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

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 200, no. 1-3, pp. 101-117.

}

TY - JOUR

T1 - Prime power divisors of binomial coefficients

AU - Erdős, P.

AU - Kolesnik, Grigori

PY - 1999/4/6

Y1 - 1999/4/6

N2 - 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.

AB - 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.

KW - Divisibility of binomial coefficients

UR - http://www.scopus.com/inward/record.url?scp=0007113392&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0007113392&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0007113392

VL - 200

SP - 101

EP - 117

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -