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- W2477552721 abstract "In this note we prove that {equation*} {np^schoose mp^s+r}equiv (-1)^{r-1}r^{-1}(m+1){nchoose m+1}p^s pmod{p^{s+1}} {equation*} where $p$ is any prime, $n$, $m$, $s$ and $r$ are nonnegative integers such that $nge m$, $sge 1$, $1le rle p^s-1$ and $r$ is not divisible by $p$. We derive a proof by induction using a multiple application of Lucas' theorem and two basic binomial coefficient identities. As an application, we prove that a similar congruence for a prime $pge 5$ established in 1992 by D. F. Bailey holds for each prime $p$." @default.
- W2477552721 created "2016-08-23" @default.
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- W2477552721 date "2012-12-29" @default.
- W2477552721 modified "2023-09-27" @default.
- W2477552721 title "Lucas Type Theorem Modulo Prime Powers" @default.
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