Fw: Euler's Phi Function

[Damien O'Rourke]

I'm just after thinking about 1.  1 is relatively prime to itself but it
would be the only positive integer.
However if we take the first definition as correct then phi(1) might be
considered meaningless as
there are no positive integers less than 0.  I suppose however, that this
could mean that
phi is equal to 0 in this case but it doesn't it equals 1.  This is
rectified in the second definition
because it is less than or equal to itself and also relatively prime to
itself which gives a value of 1
for phi(1) as expected.

Any thoughts would be great.

Regards,
Damien.


----- Original Message -----
From: "Damien O'Rourke" <orourked at eeng.dcu.ie>
To: <cryptography at wasabisystems.com>
Sent: Monday, February 24, 2003 12:54 PM
Subject: Euler's Phi Function


> Hi,
>
> I have seen two slightly different definitions for the Euler's phi
function.
> They don't cause any difference in its value
> but I was just wondering if there would be anyone who would complain about
> the use of one or the other?
>
> One says that for a positive integer n, phi(n) is the number of positive
> integers less than n and relatively prime to it.
> The other differs slightly by saying that it's the number of positive
> integers less than or equal to n and relatively prime
> to it.  Because n is not relatively prime to itself this doesn't make a
> difference in its value and using "less than or equals" seems slightly
> superfluous, however, I am writing a report and I just want to be very
> precise about the whole thing.  Thanks for your help.
>
> Regards,
> Damien.
>


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