This is exactly what i want more of on RUclips. What a delightful result. Thank you for publishing these videos. It really does feel like these sum = product identities are super useful for proofs along with chaining together inequalities. There is the R(s) = Σ(1/nˢ) = Π(1/(1 - 1/pˢ)) as a classic example of this. Also Πf(n) = e^[Σlog(f(x))] Id be really interested to explore more generalized inf sum = inf product identities like the one presented in this video in a number thory proofs context. Very fun stuff. Happy new year all!
@tedszy7100 that's awesome, the last PDF you shared on Pell's equation, quadratic irrationals, and square-triangle numbers was really well written - The problems at the end were well chosen. I will definitely make time to read over what you share.
Nice video, but I was a bit confused seeing a_j under the summation sign at 6:28 but nowhere else in the summation. I guess it means r summations over each of the exponents. I suppose one could use two summation signs with dots between them and each summation sign is for one of the exponents, with each summation going from 0 to K. Is that right?
This lecture has a very pleasant form, with handwriting. Your enthusiasm are warm and promising of much more advanced math. I can actually comprehend the proof , in spite of my fragmented [youtube] education. Thank you very much. May this new Year the best Year [yet] of this Millennium, for You and for Everyone May I ask what software you use for the handwriting?
![Noob To Max With DRAGON REWORK In Blox Fruits [FULL MOVIE]](http://i.ytimg.com/vi/LnBMOinoOvA/mqdefault.jpg)
This is exactly what i want more of on RUclips. What a delightful result. Thank you for publishing these videos.
It really does feel like these sum = product identities are super useful for proofs along with chaining together inequalities.
There is the R(s) = Σ(1/nˢ) = Π(1/(1 - 1/pˢ)) as a classic example of this.
Also Πf(n) = e^[Σlog(f(x))]
Id be really interested to explore more generalized inf sum = inf product identities like the one presented in this video in a number thory proofs context.
Very fun stuff. Happy new year all!
It's possible that i may have a scan of some old notes from many years ago about applications of prime-combinatorics identities. I will see.
@tedszy7100 that's awesome, the last PDF you shared on Pell's equation, quadratic irrationals, and square-triangle numbers was really well written - The problems at the end were well chosen. I will definitely make time to read over what you share.
Nice video, but I was a bit confused seeing a_j under the summation sign at 6:28 but nowhere else in the summation. I guess it means r summations over each of the exponents. I suppose one could use two summation signs with dots between them and each summation sign is for one of the exponents, with each summation going from 0 to K. Is that right?
Yes, that's exactly right.
What an amazing proof! Thanks for sharing.
It's just incredible how "there are a finite number of primes" would imply (if true) that "log(x) is bounded".
This lecture has a very pleasant form, with handwriting.
Your enthusiasm are warm and promising of much more advanced math.
I can actually comprehend the proof , in spite of my fragmented [youtube] education.
Thank you very much.
May this new Year the best Year [yet] of this Millennium, for You and for Everyone
May I ask what software you use for the handwriting?
Thank you for your positive and encouraging comments! I use Xjournal++.
Amazing video! Had to subscribe after this one 😮😅
Congratulations, great video 👍
Excellent
Very nice proof. Thank you for the video.
You're welcome!
Great video!!
Thanks!
Genial la prueba y la explicación
Thank you!