Pascal's triangle (mod 9)

• Autorzy: James G. Huard , Blair K. Spearman , Kenneth S. Williams
• Języki publikacji: EN

Słowa kluczowe

EN

binomial coefficients

Kategorie tematyczne

• 11A07: Congruences; primitive roots; residue systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996-1997
• Tom: 78
• Numer: 4
• Strony: 331-349

Daty

wydano

1997

otrzymano

1996-03-20

Twórcy

autor

James G. Huard

• Department of Mathematics, Canisius College, Buffalo, New York 14208, U.S.A.

autor

Blair K. Spearman

• Department of Mathematics and Statistics, Okanagan University College, Kelowna, British Columbia V1V 1V7, Canada

autor

Kenneth S. Williams

• Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada

Bibliografia

• [1] K. S. Davis and W. A. Webb, Lucas' theorem for prime powers, European J. Combin. 11 (1990), 229-233.
• [2] K. S. Davis and W. A. Webb, Pascal's triangle modulo 4, Fibonacci Quart. 29 (1991), 79-83.
• [3] J. W. L. Glaisher, On the residue of a binomial-theorem coefficient with respect to a prime modulus, Quart. J. Math. 30 (1899), 150-156.
• [4] A. Granville, Zaphod Beeblebrox's brain and the fifty-ninth row of Pascal's triangle, Amer. Math. Monthly 99 (1992), 318-331.
• [5] E. Hexel and H. Sachs, Counting residues modulo a prime in Pascal's triangle, Indian J. Math. 20 (1978), 91-105.
• [6] J. G. Huard, B. K. Spearman and K. S. Williams, Pascal's triangle (mod 8), submitted for publication.
• [7] G. S. Kazandzidis, Congruences on the binomial coefficients, Bull. Soc. Math. Grèce (NS) 9 (1968), 1-12.
• [8] E. E. Kummer, Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew. Math. 44 (1852), 93-146.
• [9] E. Lucas, Sur les congruences des nombres eulériens et des coefficients différentiels des fonctions trigonométriques, suivant un module premier, Bull. Soc. Math. France 6 (1877-8), 49-54.
• [10] W. A. Webb, The number of binomial coefficients in residue classes modulo p and p², Colloq. Math. 60/61 (1990), 275-280.