Talk:Carmichael function

message: I'm afraid that Lower Bound in Theorem 1 makes very little sense. Are you sure that everything is perfectly OK?
And why this page is - well - extremele similar to that on answers.com?
http://www.answers.com/topic/carmichael-function
: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 Battie 11:59, 11 October 2006 (UTC)
replies: text: 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)
thread_title: Lower Bound in Theorem 1 makes very little sense

message: 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)
replies: text: In the case of p = 2, let a be coprime with respect to p; that is, a = 1 + 2n. One can immediately obtain a^1 \equiv 1 \text{ mod 2}, where the Euler's totient function of 2, \psi(2), is equal to 1. Thus, a^{\psi(2)} \equiv 1 \text{ mod 2}. Likewise, in the case of p = 4, let a be coprime with respect to p; that is, either a = 1 + 4n or a = 3 + 4n. In the first case, a^1 \equiv 1 \text{ mod 4}. In the second case, a^1 \equiv 3 \text{ mod 4}, and a^2 \equiv 9 \equiv 1 \text{ mod 4}, where the Euler's totient function of 4, \psi(4), is equal to 2. Therefore, a^{\psi(4)} \equiv 1 \text{ mod 4}. D4nn0v (talk) 04:24, 15 January 2018 (UTC)
thread_title: recursive definition of the function is incomplete

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thread_title:  External links modified 

message: Values for 15 and 16 are shown in bold indicating they are different when the actual values shown seem to match.
--N8 08:06, 31 August 2018 (UTC)
thread_title:  Table of first values inconsistent