Premium Only Content

Arithmetic derivative: an introduction | number theory | advanced level
Episode 100.
Arithmetic derivative: an introduction | number theory | advanced level.
Branch of mathematics: number theory.
Difficulty level: advanced.
The arithmetic derivative is a function $D$ from natural numbers to natural numbers defined by the 2 propeties:
1. For any prine number $p$, we have $D(p)=1$.
2. For any 2 natural numbers $m$ and $n$, we have $D(m \cdot n) = D(m) \cdot n + m \cdot D(n)$.
There is also an explicit formula. If $n = \prod_{i}{p_i}$ is the representation of $n$ as a product of its prime divisors (some of them could be duplicated), then $D(n)=n \sum_{i}{\frac{1}{p_i}}$.
Mathematics. Number theory.
#Mathematics #NumberTheory
tags:
mathematics,number theory,prime,prime number,arithmetic derivative,derivative,differentiate,differentiation,product rule
The same video on YouTube:
https://youtu.be/YqoP1ZrkKAA
The same video on Telegram:
https://t.me/mathematical_bunker/124
-
LIVE
VOPUSARADIO
1 day agoPOLITI-SHOCK! "DESTROY THE NARRATIVE & EXPOSE THE FRAUDS" W/ Special Guest Timothy Shea
323 watching -
1:24:25
Glenn Greenwald
6 hours agoGame of Thrones Actor Liam Cunningham on Gaza Activism and UK Censorship; Journalist Zaid Jilani on Mamdani, Epstein, the State of the Dems, and More | SYSTEM UPDATE #484
116K35 -
2:48:13
Nikko Ortiz
6 hours agoGas Station Shooting Gone Wrong
54.6K8 -
1:45:00
RiftTV
5 hours agoBETRAYAL: Bondi Persecutes HERO DOCTOR Under Trump DOJ | The Rift | Marc Lobliner & Lilly Gaddis
35.3K15 -
7:29:03
RalliedLIVE
10 hours ago $3.65 earnedSHOTTY BOYS vs TRIPLE THREAT THURSDAY
66.9K2 -
1:21:59
Donald Trump Jr.
6 hours agoButler: The Untold Story, Interview with Salena Zito | TRIGGERED Ep.257
159K116 -
1:00:56
BonginoReport
7 hours agoBen Shapiro Wants You To Move On From Epstein - Nightly Scroll w/ Hayley Caronia (Ep.87)
88.5K111 -
34:40
ZeeeMedia
6 hours agoFDA's Shock mRNA Approval, Millions of Epstein Docs, ICE MASSIVE Pedo Bust | Daily Pulse Ep 64
40.1K26 -
12:41
Dad Saves America
7 hours ago $1.14 earnedThe Poisoning of the American Mind: School Doesn’t Prepare Kids for Adulthood - Pt 1
29K3 -
2:06:39
Quite Frankly
11 hours ago"New Media Disillusion & Doom Cycle Therapy" ft. Jon Herold 7/10/25
28.4K11