A partial solution to the
Erdös Squarefree Conjecture which states that the
Binomial Coefficient is never Squarefree for all sufficiently large .
Sárközy (1985) showed that if is the square part of the Binomial Coefficient ,
then
See also Binomial Coefficient, Erdös Squarefree Conjecture
References
Erdös, P. and Graham, R. L. Old and New Problems and Results in Combinatorial Number Theory.
Geneva, Switzerland: L'Enseignement
Mathématique Université de Genève, Vol. 28, 1980.
Sander, J. W. ``A Story of Binomial Coefficients and Primes.'' Amer. Math. Monthly 102, 802-807, 1995.
Sárközy, A. ``On the Divisors of Binomial Coefficients, I.'' J. Number Th. 20, 70-80, 1985.
Vardi, I. ``Applications to Binomial Coefficients.'' Computational Recreations in Mathematica.
Reading, MA: Addison-Wesley, pp. 25-28, 1991.