Everule's blog

By Everule, history, 13 months ago, In English

Lucas theorem deals with analyzing the structure of $$$\binom{n}{r} \mod p$$$ for prime $$$p$$$. $$$\binom{n}{r}$$$ is odd if and only if $$$r$$$ is a submask of $$$n$$$. If that doesn't catch your attention probably this blog isn't for you ...

Case 1: $$$n = p$$$

Combinatorial interpretation
Algebraic interpretation

Case 2: $$$n = p^t$$$

Combinatorial Interpretation
Algebraic Interpretation

Case 3: $$$n = \sum_t d_t \times p^t$$$

Combinatorial Interpretation
Algebraic Interpretation
Example problem to use the internal operation instead of the final result
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13 months ago, # |
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is p prime?

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13 months ago, # |
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Yet another geniosity blog

Btw, for anyone interested, here is the object that is actually described in case 1

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13 months ago, # |
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Thanks for posting.