What Is the Proizvolov's Identity and How You Can Prove It!
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- čas přidán 3. 08. 2024
- Proizvolov's Identity is an identity concerning sums of differences of positive integers. It is proposed by Vyacheslav Proizvolov as a problem in the 1985 All-Union Soviet Student Olympiads. In this video, we will be proving this identity in two different ways and the only way to know how to prove it is to watch all the way to the end of the video.
Video Chapters:
0:00 What Is The Proizvolov's Identity?
1:06 First Proof
5:55 Second Proof
8:16 Outro + Subscribe!
*Corrections: (I'm terribly sorry for the typos)
1:44 It should be "1" less than i less than j
4:41 The second b_{j+1} should be b_{j+2} instead
5:00 The b_{j-2} should be b_{j-1}
Proizvolov's Identity (Wikipedia):
en.wikipedia.org/wiki/Proizvo...
Cut The Knot:
www.cut-the-knot.org/Curricul...
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I have added some extra captions and animations to the video, what do you think? Feel free to give feedbacks and suggestions.
Also, I'm terribly sorry for the typos being made:
1:44 It should be "1" less than i less than j
4:41 The second b_{j+1} should be b_{j+2} instead
5:00 The b_{j-2} should be b_{j-1}
I know this identity but didn't know the name of this identity
Are you currently a high school math teacher? You sound rly similar to a teacher I had last semester
I'm actually a college student, studying A levels :)
@@1psi3colourmath oh cool & nice! That makes sense. U do sound a bit younger than him, but there was still a strong resemblance.