Need help understanding how Euler's totient function works.

J

Joshua David

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In this proof for Euler's totient function, it is claimed that "[math]\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,[/math]" but I have a difficulty understanding why. Can somebody explain this to me? Thanks in advance!
 
Joshua David said:
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!
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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 [imath]p_i[/imath]...", not "divisible by n".
 
@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
 
Steven G said:
@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
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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
 
topsquark said:
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
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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 said:
Completely unrelated to the topic, but: why "He"? English is mostly gender-neutral, so what made you choose this pronoun?
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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
 
topsquark said:
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
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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 :)
 
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