Need help understanding how Euler's totient function works.

[Joshua David]

In this proof for Euler's totient function, it is claimed that "$$\text{The number of integers from 1 to n that are divisible by n is simply} \frac{n}{p_i}, \text{since } p_i \text{ divides } n,$$" but I have a difficulty understanding why. Can somebody explain this to me? Thanks in advance!

 

[blamocur]

In this proof for Euler's totient function, it is claimed that "The number of integers from 1 to n that are divisible by n is simplynpi,since pi divides n,\text{The number of integers from 1 to n that are divisible by n is simply} \frac{n}{p_i}, \text{since } p_i \text{ divides } n,The number of integers from 1 to n that are divisible by n is simplypin,since pi divides n," but I have a difficulty understanding why. Can somebody explain this to me? Thanks in advance!

I think you've found a typo in the text. I am sure they meant "the number of integers from 1 to n that are divisible by $p_i$...", not "divisible by n".

 

[Steven G]

@blamocur,
Congrats for surviving your first year here. It take a different type of person to do that. You get to decide what different means.
Steve

 

[topsquark]

@blamocur,
Congrats for surviving your first year here. It take a different type of person to do that. You get to decide what different means.
Steve

Ummm... Steve? Look at the date again. He started here two years ago!

I'm out of the corner. You can have my dunce cap back for a while, if you like!

-Dan

 

[Steven G]

Ummm... Steve? Look at the date again. He started here two years ago!

I'm out of the corner. You can have my dunce cap back for a while, if you like!

-Dan

I really do need to concentrate a bit more. Yep, it is two years. I would use your dunce cap but it must be completely worn out by now. Besides, I would need the cap for more than a while--at least a long while.

 

[blamocur]

I really do need to concentrate a bit more.

I've been reminding that to myself for two years And thanks anyway!

 

[blamocur]

He started here two years ago

Completely unrelated to the topic, but: why "He"? English is mostly gender-neutral, so what made you choose this pronoun?

 

[topsquark]

Completely unrelated to the topic, but: why "He"? English is mostly gender-neutral, so what made you choose this pronoun?

Please understand, I don't mean anything by it. I should have caught that. My apologies if you are a woman. I grew up in the 70s and my diction hasn't found a way to cope with avoiding gender comments too well. (And, honestly, with all the possibilities now-a-days, I'm afraid that I've gotten a bit lazy about it.)

-Dan

 

[blamocur]

Please understand, I don't mean anything by it. I should have caught that. My apologies if you are a woman. I grew up in the 70s and my diction hasn't found a way to cope with avoiding gender comments too well. (And, honestly, with all the possibilities now-a-days, I'm afraid that I've gotten a bit lazy about it.)

-Dan

No offense whatsoever, and no need for apology -- just pure curiosity on my part. And, BTW, your guess is correct. My avatar, on the other hand, is female, but she is not offended either