Lucas’ theorem for extended generalized binomial coefficients

R. L. Ollerton and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 12, 2006, Number 2, Pages 8–12
Full paper (PDF, 39 Kb)

Details

Authors and affiliations

R. L. Ollerton
University of Western Sydney, Penrith Campus DC1797, Australia

A. G. Shannon
KvB Institute of Technology, North Sydney 2060, and
Warrane College, The University of NSW, Kensington 1465, Australia

AMS Classification

• 11A07
• 11A41
• 11B65

References

1. R.C. Bollinger & C. L. Burchard. “Lucas’s theorem and some related results for extended Pascal triangles.” American Mathematical Monthly 97.3 (1990):198-204.
2. L. Carlitz. “Some congruences involving sums of binomial coefficients.” Duke Math. J. 27.1 (1960):77-80.
3. L. Carlitz. “Some congruences involving binomial coefficients.” Duke Math. J. 33.4 (1966):721-724.
4. R.L. Ollerton & A.G. Shannon. “Extensions of generalized binomial coefficients.” Applications of Fibonacci Numbers 9:187-199, 2004.
5. R.L. Ollerton & A.G. Shannon. “Further properties of generalized binomial coefficient k-extensions.” Fibonacci Quarterly, 43(2):124-129, 2005.
6. D.G. Poole. “The Towers and Triangles of Professor Claus (or, Pascal Knows Hanoi).” Math. Mag. 67 (1994):323-344.