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The answers.com link refs wikipedia as the source so their info came from here rather than the other way around. I do find the article very difficult to follow though so a rewrite might be a good idea.
Maddog Battie11:59, 11 October 2006 (UTC)reply
And then there is the section that is called "Average and Typical value", but with no explanation of what these really mean, and what is the distinction between the two. In many mathematical, statistical, and scientific, and engineering applications, the average value and the typical value are one and the same. (So, there would be no reason to mention both of them.) On the other hand, there are situations where the average value exists, but some other value (such as possibly some median value) is more "typical". Also, there are some cases, such as where we have a Cauchy-distributed random variable, where the average value does not exist mathematically, but there is a "typical" value that can be defined. It might be a median, or a value of maximum likelihood, or to get more technical, it could be the "Cauchy Principal Value" of the average. Note that the Cauchy Principal Value of something is not just for Cauchy random variables, but it is a more general concept that can be applied to lots of infinite sums and indefinite integrals.
72.146.44.141 (
talk)
15:58, 6 October 2008 (UTC)reply
recursive definition of the function is incomplete
I think the recursive definition of the function is incomplete. What to do with the cases p = 2^1 and p = 2^2 ? The example sequence (1,1,2,2,...) indicates these ones fall in the general p^(k-1)*(p-1) case. I'm no mathematician, could a math guy (or girl) fix this? —Preceding
unsigned comment added by
Rkomatsu (
talk •
contribs)
11:15, 10 March 2010 (UTC)reply
In the case of , let be coprime with respect to ; that is, . One can immediately obtain , where the Euler's totient function of , , is equal to . Thus, . Likewise, in the case of , let be coprime with respect to ; that is, either or . In the first case, . In the second case, , and , where the Euler's totient function of , , is equal to . Therefore, .
D4nn0v (
talk)
04:24, 15 January 2018 (UTC)reply
phrase doesn't seem to be necessary
In the phrase "for every integer a that is both coprime to and smaller than n." the limitation "smaller than n." doesn't seem to be necessary. a^m mod n = 1 is valid for any integer a coprime to n, according to at least one other source. I ask a math expert to verify this, I don't know whether this is a mistake or simply a more recent result not included in the original definition of the Carmichael function.
Rkomatsu (
talk)
14:18, 10 March 2010 (UTC)reply
You are right, the statements
for every integer a that is coprime to n
and
for every integer a that is both coprime to and smaller than n
and
for every positive integer a that is both coprime to and smaller than n
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