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Polynomials that generate a row of Pascal's triangle

Authors
김선홍
Issue Date
Jul-2002
Publisher
대한수학회
Keywords
Pascal's triangle; Lagrange interpolation
Citation
대한수학회논문집, v.17, no.3, pp 383 - 387
Pages
5
Journal Title
대한수학회논문집
Volume
17
Number
3
Start Page
383
End Page
387
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/10377
DOI
10.4134/CKMS.2002.17.3.383
ISSN
1225-1763
2234-3024
Abstract
Let $p$ be an odd prime, and let $f(x)$ be theinterpolating polynomial associated with a table of data points$(j+1, \binom {p}{j})$ for $0 \leq j \leq p$. In this article, wefind congruence identities modulo $p$ of $(p-1)! \, f(x)$, $(p-2)!\, f(x)$, and $(p-3)! \, f(x)$. Moreover we present someconjectures of these types. .
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