Erdős Squarefree Conjecture
المؤلف:
Erdős, P. and Graham, R. L.
المصدر:
Old and New Problems and Results in Combinatorial Number Theory. Geneva, Switzerland: L,Enseignement Mathématique Université de Genève, Vol. 28
الجزء والصفحة:
...
1-8-2020
1950
Erdős Squarefree Conjecture
The central binomial coefficient 
is never squarefree for 
. This was proved true for all sufficiently large 
by Sárkőzy's theorem. Goetgheluck (1988) proved the conjecture true for 
and Vardi (1991) for 
. The conjecture was proved true in its entirety by Granville and Ramare (1996).
REFERENCES:
Erdős, 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.
Sárkőzy, 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.
الاكثر قراءة في نظرية الاعداد
اخر الاخبار
اخبار العتبة العباسية المقدسة
