Lucas Theorem is not an equation, it's an operation!

Правка en1, от Everule, 2023-10-03 04:45:17

Lucas theorem deals with analyzing the structure of $$$\binom{n}{r} \mod p$$$. $$$\binom{n}{r}$$$ 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

История

 
 
 
 
Правки
 
 
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en2 Английский Everule 2023-10-03 04:55:15 28 Tiny change: 'r} \mod p$. $\bino' -> 'r} \mod p$ for prime $p$. $\bino'
en1 Английский Everule 2023-10-03 04:45:17 5967 Initial revision (published)