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

where is the Riemann Zeta Function. An upper bound on of has been obtained.

**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.

© 1996-9

1999-05-26