Check out Prof. Omar's video on the next problem in the series: ruclips.net/video/8v_sh7JMUS0/видео.html Also, minor mistake at 2:48, it should be "k is a factor of n".
This is lovely, particularly the way you scaffold up from simplest inputs to more complex ones. When I've taught this convolution, I've always just used n=12, to have a concrete example that has multiple prime factors and a square factor too. I'm going to use your approach in the future. 🤩
That is very interesting, do you have other videos about Dirichet convolution and can you do more videos about arithmetic functions and analytic Number Theory?
I'm not sure what the question-writers had in mind! However, we know that no function with f(1) = 0 has an inverse. That's because (f * f⁻¹)(1) = ϵ(1) = 1 by definition. We know that (f * f⁻¹)(1) = f(1)f⁻¹(1) but if f(1) = 0, then that means (f * f⁻¹)(1) = 0, so there's no way to get 1 as the output!
Check out Prof. Omar's video on the next problem in the series: ruclips.net/video/8v_sh7JMUS0/видео.html
Also, minor mistake at 2:48, it should be "k is a factor of n".
This is lovely, particularly the way you scaffold up from simplest inputs to more complex ones. When I've taught this convolution, I've always just used n=12, to have a concrete example that has multiple prime factors and a square factor too. I'm going to use your approach in the future. 🤩
Very interesting. Never heard about Durichlet convolution before.☺
After watching the second video by profomarmath, i have to admit, that i liked his a little more. Loved both of them though.
That is very interesting, do you have other videos about Dirichet convolution and can you do more videos about arithmetic functions and analytic Number Theory?
Saved my day
Nice work
I really like these videos. Btw, what college are you going to?
I will go to Caltech starting this fall!
How can i contact with you
I have a problems can you help me
What about the class of functions that give f(1)=0? Why do they ask for the inverses without excluding them from the question?
I'm not sure what the question-writers had in mind! However, we know that no function with f(1) = 0 has an inverse. That's because (f * f⁻¹)(1) = ϵ(1) = 1 by definition. We know that
(f * f⁻¹)(1) = f(1)f⁻¹(1)
but if f(1) = 0, then that means (f * f⁻¹)(1) = 0, so there's no way to get 1 as the output!
Your are amazing bro
Hi
Trivial
explanation is very bad
Hi