论文信息 - BINOMIAL COEFFICIENTS GENERALIZED WITH RESPECT TO A DISCRETE VALUATION

BINOMIAL COEFFICIENTS GENERALIZED WITH RESPECT TO A DISCRETE VALUATION

There is a fine Theorem of Kummer on the power to which a prime appears in the prime factorization of a binomial coefficient: Theorem: (Kummer [10]) If p is a prime, then the exact power of p dividing the binomial coefficient( n k ) is equal to the number of carries that occur in the addition of k and n — k in base p arithmetic.

Sophie Frisch | S. Frisch

[1] P. Cahen. Polynomes a Valeurs Entieres , 1972, Canadian Journal of Mathematics.

[2] Miles Reid,et al. Commutative ring theory: Frontmatter , 1987 .

[3] Sophie Frisch,et al. Interpolation by Integer-Valued Polynomials☆ , 1999 .

[4] P. Cahen. Integer-valued polynomials on a subset , 1993 .

[5] Donald Ervin Knuth,et al. The Art of Computer Programming , 1968 .

[6] Donald L. Mcquillan. On Prüfer domains of polynomials. , 1985 .

[7] B. M. Fulk. MATH , 1992 .

[8] David Singmaster,et al. Notes on Binomial Coefficients I—A Generalization of Lucas' Congruence , 1974 .

[9] E. Kummer. Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen. , 1852 .

[10] David Singmaster. Notes on Binomial Coefficients Iii—Any Integer Divides Almost All Binomial Coefficients† , 1974 .

[11] G. Pólya,et al. Über ganzwertige Polynome in algebraischen Zahlkörpern. , 1919 .

[12] R. Gilmer,et al. The Noetherian property in rings of integer-valued polynomials , 1993 .

[13] S. Frisch. Integer-valued polynomials on Krull rings , 1994 .

[14] J. Chabert. Le groupe de Picard de l'anneau des polynômes à valeurs entières , 1992 .

[15] Hiroshi Gunji,et al. On a class of ideals in an algebraic number field , 1970 .

[16] Donald E. Knuth,et al. The power of a prime that divides a generalized binomial coefficient. , 1989 .