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An extension of Lucas’ theorem (2001)
by
Hong Hu
,
Zhi-wei Sun
| Venue: | PROC. AMER. MATH. SOC |
| Citations: | 21 - 14 self |
BibTeX
@ARTICLE{Hu01anextension,
author = {Hong Hu and Zhi-wei Sun},
title = {An extension of Lucas’ theorem},
journal = {PROC. AMER. MATH. SOC},
year = {2001},
pages = {3471--3478}
}
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Abstract
Let p be a prime. A famous theorem of Lucas states that ( mp+s) ≡ ( np+t m) ( s) (mod p) ifm, n, s, t are nonnegative integers with s, t < p. Inthispaper n t we aim to prove a similar result for generalized binomial coefficients defined in terms of second order recurrent sequences with initial values 0 and 1.
