Sárközy's Theorem
A partial solution to the Erdös Squarefree Conjecture which states that theBinomial 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.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.
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