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Estimates of the least prime factor of a binomial coefficient

Part of: Sequences and sets

Published online by Cambridge University Press:  26 February 2010

S. V. Konyagin
S. V. Konyagin
Affiliation:
Dept. of Mech. and Math., Moscow State University, Moscow, 119899, Russia. e-mail: kon@nw.math.msu.su
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Abstract

Let k be a positive integer and g(k) be the least integer n > k + 1 such that all prime factors of are >k. We prove that

where c is an absolute positive constant. We also establish a new theorem on the distribution of fractional parts of a smooth function.

MSC classification

Secondary: 11B65: Binomial coefficients; factorials; $q$-identities
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 41 - 55
Copyright
Copyright © University College London 1999

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