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On Prime Divisors of Binomial Coefficients

✍ 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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Prime power divisors of binomial coeffic
✍ Paul ErdΓΆs; Grigori Kolesnik πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 582 KB

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

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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