Citation
H. Hu et Zw. Sun, An extension of Lucas' theorem, P AM MATH S, 129(12), 2001, pp. 3471-3478
Citations number
10
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939
→ ACNP
Volume
129
Issue
12
Year of publication
2001
Pages
3471 - 3478
Database
ISI
SICI code
0002-9939(2001)129:12<3471:AEOLT>2.0.ZU;2-6
Abstract
Let p be a prime. A famous theorem of Lucas states that ((mp+s)(np+t)) n= (
m)(n) ((t) (s)) (mod p) if m, n, s, t are nonnegative integers with s, t <
p. In this paper we aim to prove a similar result for generalized binomial
coefficients defined in terms of second order recurrent sequences with init
ial values 0 and 1.