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On Prime Divisors of Binomial Coefficients

On Prime Divisors of Binomial Coefficients In 1985, Sárközy proved a conjecture of Erdös by showing that (2nn) is never square‐free for sufficiently large n. By applying a new estimate on exponential sums, we prove that this also holds for (2n±dn) if dis not ‘too big’. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

On Prime Divisors of Binomial Coefficients

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/24.2.140
Publisher site
See Article on Publisher Site

Abstract

In 1985, Sárközy proved a conjecture of Erdös by showing that (2nn) is never square‐free for sufficiently large n. By applying a new estimate on exponential sums, we prove that this also holds for (2n±dn) if dis not ‘too big’.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Mar 1, 1992

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