Polynomials that generate a row of Pascal's triangle

초록

Let $p$ be an odd prime, and let $f(x)$ be theinterpolating polynomial associated with a table of data points$(j+1,(\genfrac{}{}{0ex}{}{p}{j}))$ for $0\le j\le p$. 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. .

키워드