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Prime power divisors of binomial coefficients

✍ Scribed by Paul Erdös; Grigori Kolesnik

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
582 KB
Volume
200
Category
Article
ISSN
0012-365X

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✦ Synopsis

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 some other results on divisibility of binomial coefficients. (~) 1999 Elsevier Science B.V.

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A Binomial Coefficient Congruence Modulo
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Prime Power Divisors of Multinomial and
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✍ Grigori Kolesnik 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 151 KB

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