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On the scarcity of powerful binomial coefficients

Part of:Sequences and sets

Published online by Cambridge University Press:  26 February 2010

Andrew Granville
Andrew Granville
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, U.S.A. E-mail: andrew@math.uga.edu
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Abstract

Assuming the abc-conjecture, it is shown that there are only finitely many powerful binomial coefficients with 3≤k≤n/2 in fact, if q2 divides , then . Unconditionally, it is shown that there are N1/2+σ(1) powerful binomial coefficients in the top N rows of Pascal's Triangle.

MSC classification

Secondary:11B65: Binomial coefficients; factorials; $q$-identities

Information

Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999, pp. 397 - 410
Copyright
Copyright © University College London 1999

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