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Lucas' Theorem

Revision as of 10:50, 8 November 2007 by Minsoens (talk | contribs) (New page: Let <math>p</math> be a prime. If <math>(\overline{n_mn_{m-1}\cdots n_0})_p</math> is the base <math>p</math> representation of <math>n</math> and <math>(\overline{i_mi_{m-1}\cdots i_0})_p...)
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Let $p$ be a prime. If $(\overline{n_mn_{m-1}\cdots n_0})_p$ is the base $p$ representation of $n$ and $(\overline{i_mi_{m-1}\cdots i_0})_p$ is the base $p$ representation of $i$, where $n\geq i$, Lucas' Theorem states that \[\binom{n}{i}\equiv \prod_{j=0}^{m}\binom{n_j}{i_j}\pmod{p}\]

Proof

Links

See also

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