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

Revision en1, by 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

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en2 English Everule 2023-10-03 04:55:15 28 Tiny change: 'r} \mod p$. $\bino' -> 'r} \mod p$ for prime $p$. $\bino'
en1 English Everule 2023-10-03 04:45:17 5967 Initial revision (published)