Erdös Squarefree Conjecture

The Central Binomial Coefficient is never Squarefree for . This was proved true for allsufficiently large by Sárközy's Theorem. Goetgheluck (1988) proved the Conjecturetrue for and Vardi (1991) for . The conjecture was proved true in its entirely byGranville and Ramare (1996).

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, p. 71, 1980.

Goetgheluck, P. ``Prime Divisors of Binomial Coefficients.'' Math. Comput. 51, 325-329, 1988.

Granville, A. and Ramare, O. ``Explicit Bounds on Exponential Sums and the Scarcity of Squarefree Binomial Coefficients.'' Mathematika 43, 73-107, 1996.

Sander, J. W. ``On Prime Divisors of Binomial Coefficients.'' Bull. London Math. Soc. 24, 140-142, 1992.

Sander, J. W. ``A Story of Binomial Coefficients and Primes.'' Amer. Math. Monthly 102, 802-807, 1995.

Sárközy, A. ``On 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.

• Sines Law
• Sine-Tangent Theorem
• Singly Even Number
• Singular Homology
• Singularity
• Singular Point (Algebraic Curve)
• Singular Point (Differential Equation)
• Singular Point (Function)
• Singular Series
• Singular System
• Singular Value
• Singular Value Decomposition
• Sinh
• Sink (Directed Graph)
• Sink (Map)
• Sinusoidal Projection
• Sinusoidal Spiral
• Sinusoidal Spiral Inverse Curve
• Sinusoidal Spiral Pedal Curve
• Sister Celine's Method
• Site Percolation
• Siteswap
• Six-Color Theorem
• Skein Relationship
• Skeleton