Skip to content

Cite Legendre's Formula (#1019) #1029

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 1 commit into from
Jan 29, 2023
Merged

Cite Legendre's Formula (#1019) #1029

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
1 change: 1 addition & 0 deletions src/algebra/factorial-divisors.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -24,6 +24,7 @@ The final answer is

$$\Bigl\lfloor\dfrac{n}{k}\Bigr\rfloor + \Bigl\lfloor\dfrac{n}{k^2}\Bigr\rfloor + \ldots + \Bigl\lfloor\dfrac{n}{k^i}\Bigr\rfloor + \ldots$$

This result is also known as [Legendre's formula](https://en.wikipedia.org/wiki/Legendre%27s_formula).
The sum is of course finite, since only approximately the first $\log_k n$ elements are not zeros. Thus, the runtime of this algorithm is $O(\log_k n)$.

### Implementation
Expand Down