It is known that for sufficiently large n and m and any r the binomial coefficient (~) which is close to the middle coefficient is divisible by pr where p is a 'large' prime. We prove the exact divisibility of (,~) by p' for p>c(n). The lower bound is essentially the best possible. We also prove som
β¦ LIBER β¦
On Prime Divisors of Binomial Coefficients
β Scribed by Sander, J. W.
- Book ID
- 120091865
- Publisher
- Oxford University Press
- Year
- 1992
- Tongue
- English
- Weight
- 60 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0024-6093
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We prove that for any integer d multinomial coefficients satisfying some conditions are exactly divisible by p d for many large primes p. The obtained results are essentially the best possible. Also, we show that under some hypothesis q-multinomial coefficients are divisible by p d . ## 2001 Academ