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Subprime Factorization and the Numbers of Binomial Coefficients Exactly Divided by Powers of a Prime

William B. Everett
Published Online: 2012-03-27 | DOI: https://doi.org/10.1515/integ.2011.101


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.

Keywords.: Binomial Coefficients; Subprime Factorization; Self-Similarity

About the article

Received: 2010-09-04

Revised: 2011-07-26

Accepted: 2011-09-29

Published Online: 2012-03-27

Published in Print: 2012-04-01

Citation Information: Integers, Volume 12, Issue 2, Pages 259–274, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integ.2011.101.

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