An extension of Lucas' theorem

Authors:
Hong Hu and Zhi-Wei Sun

Journal:
Proc. Amer. Math. Soc. **129** (2001), 3471-3478

MSC (2000):
Primary 11B39; Secondary 11A07, 11B65

Published electronically:
June 8, 2001

MathSciNet review:
1860478

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Let be a prime. A famous theorem of Lucas states that if are nonnegative integers with . In this paper we aim to prove a similar result for generalized binomial coefficients defined in terms of second order recurrent sequences with initial values and .

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Additional Information

**Hong Hu**

Affiliation:
Department of Mathematics, Huaiyin Normal College, Huaiyin 223001, Jiangsu Province, People’s Republic of China

**Zhi-Wei Sun**

Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China

Email:
zwsun@nju.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-01-06234-7

Received by editor(s):
April 18, 2000

Published electronically:
June 8, 2001

Additional Notes:
The second author is responsible for all the communications, and supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, and the National Natural Science Foundation of P. R. China.

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2001
American Mathematical Society