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Pascal's Triangle (mod 8)

✍ Scribed by James G. Huard; Blair K. Spearman; Kenneth S. Williams

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 257 KB
Volume: 19
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1997.0146

No coin nor oath required. For personal study only.

✦ Synopsis

Lucas' theorem gives a congruence for a binomial coefficient modulo a prime. Davis and Webb (Europ. J. Combinatorics, 11 (1990), 229-233) extended Lucas' theorem to a prime power modulus. Making use of their result, we count the number of times each residue class occurs in the nth row of Pascal's triangle (mod 8). Our results correct and extend those of Granville (Amer. Math. Monthly, 99 (1992), 318-331).

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