a1 Department of Mathematics, University of Georgia, Athens, Georgia 30602, U.S.A. e-mail email@example.com
a2 Université Nancy I, 54506 Vandoeuvre-les-Nancy, France. e-mail firstname.lastname@example.org
The distribution of squarefree binomial coefficients. For many years, Paul Erdős has asked intriguing questions concerning the prime divisors of binomial coefficients, and the powers to which they appear. It is evident that, if k is not too small, then must be highly composite in that it contains many prime factors and often to high powers. It is therefore of interest to enquire as to how infrequently is squarefree. One well-known conjecture, due to Erdős, is that is not squarefree once n > 4. Sarközy [Sz] proved this for sufficiently large n but here we return to and solve the original question.
(Received June 20 1994)