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Subprime Factorization and the Numbers of Binomial Coefficients Exactly Divided by Powers of a Prime
-
William B. Everett
Published/Copyright:
March 27, 2012
Abstract.
We use the notion of subprime factorization to establish recurrence
relations for the number of binomial coefficients in a given row of Pascal's
triangle that are divisible by 
and not divisible by 
, where
is a prime. Using these relations to compute this number can provide
significant savings in the number of computational steps.
Received: 2010-09-04
Revised: 2011-07-26
Accepted: 2011-09-29
Published Online: 2012-03-27
Published in Print: 2012-April
© 2012 by Walter de Gruyter Berlin Boston
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- Odd Catalan Numbers Modulo
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- Diophantine Equations of Matching Games I
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- A New Proof of Winquist's Identity
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- Codes Associated with and Power Moments of Kloosterman Sums
- Subprime Factorization and the Numbers of Binomial Coefficients Exactly Divided by Powers of a Prime
- Generalized Nonaveraging Integer Sequences
- The Robin Inequality for 7-Free Integers
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Articles in the same Issue
- Masthead
- Odd Catalan Numbers Modulo
- Variations of the Poincaré Map
- Diophantine Equations of Matching Games I
- Norm Euclidean Quaternionic Orders
- A New Proof of Winquist's Identity
- Counting Depth Zero Patterns in Ballot Paths
- Codes Associated with and Power Moments of Kloosterman Sums
- Subprime Factorization and the Numbers of Binomial Coefficients Exactly Divided by Powers of a Prime
- Generalized Nonaveraging Integer Sequences
- The Robin Inequality for 7-Free Integers
- On 3-adic Valuations of Generalized Harmonic Numbers
