Pascal's triangle (mod 9)

James G. Huard; Blair K. Spearman; Kenneth S. Williams

Acta Arithmetica (1997)

  • Volume: 78, Issue: 4, page 331-349
  • ISSN: 0065-1036

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James G. Huard, Blair K. Spearman, and Kenneth S. Williams. "Pascal's triangle (mod 9)." Acta Arithmetica 78.4 (1997): 331-349. <http://eudml.org/doc/206954>.

@article{JamesG1997,
author = {James G. Huard, Blair K. Spearman, Kenneth S. Williams},
journal = {Acta Arithmetica},
keywords = {binomial coefficients; congruences; Pascal triangle},
language = {eng},
number = {4},
pages = {331-349},
title = {Pascal's triangle (mod 9)},
url = {http://eudml.org/doc/206954},
volume = {78},
year = {1997},
}

TY - JOUR
AU - James G. Huard
AU - Blair K. Spearman
AU - Kenneth S. Williams
TI - Pascal's triangle (mod 9)
JO - Acta Arithmetica
PY - 1997
VL - 78
IS - 4
SP - 331
EP - 349
LA - eng
KW - binomial coefficients; congruences; Pascal triangle
UR - http://eudml.org/doc/206954
ER -

References

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  1. [1] K. S. Davis and W. A. Webb, Lucas' theorem for prime powers, European J. Combin. 11 (1990), 229-233. Zbl0704.11002
  2. [2] K. S. Davis and W. A. Webb, Pascal's triangle modulo 4, Fibonacci Quart. 29 (1991), 79-83. Zbl0732.11009
  3. [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. Zbl29.0152.03
  4. [4] A. Granville, Zaphod Beeblebrox's brain and the fifty-ninth row of Pascal's triangle, Amer. Math. Monthly 99 (1992), 318-331. Zbl0757.05003
  5. [5] E. Hexel and H. Sachs, Counting residues modulo a prime in Pascal's triangle, Indian J. Math. 20 (1978), 91-105. Zbl0499.10005
  6. [6] J. G. Huard, B. K. Spearman and K. S. Williams, Pascal's triangle (mod 8), submitted for publication. 
  7. [7] G. S. Kazandzidis, Congruences on the binomial coefficients, Bull. Soc. Math. Grèce (NS) 9 (1968), 1-12. 
  8. [8] E. E. Kummer, Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew. Math. 44 (1852), 93-146. 
  9. [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. [10] W. A. Webb, The number of binomial coefficients in residue classes modulo p and p², Colloq. Math. 60/61 (1990), 275-280. Zbl0734.11018

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