Talk:Proofs of Fermat's little theorem

message: The example given is 2x2=5x2 (mod 6) which is all well and good, but six isn't even relatively prime to two, so I'd recommend a different example. If I can think of one in the next four minutes I'll do it myself, otherwise I have to leave and will probably forget.
:Never mind, I'm an idiot. I seem to have forgotten division by a relative prime is well defined in modular arithmetic (I have been working WAY to hard if I've forgotten that). Still I think something concerning this fact should be mentioned in the article under why division using modular arithmetic is only justified when dividing by numbers relatively prime to the modulo.Guardian of Light 17:53, 22 December 2005 (UTC)
thread_title:  on the justification of using a prime 

message: Lemma 1 proves that there are n fixed points, not n+1:  the fixed point 1 is counted twice.  The proof still works given this correction since (a^p +1) - (a+1) = a^p - a. —The preceding unsigned comment was added by 203.173.167.211 (talk) 04:37, 7 April 2007 (UTC)
thread_title:  Error in dynamical system proof 

message: While my last math class was high school math, it seems to me that the bracelet proof is included twice, once without illustrations, and once with. If I'm wrong, and these are two distinct proofs, then I think this needs to be clarified. Otherwise, I'd say, keep the one with pictures.
-- trlkly 12:35, 1 June 2007 (UTC)
thread_title:  Two bracelet proofs 

message: I'm too tired now to fully check the details, but it looks to me like that the fact that T_n is defined at 1 is inessential; and since it's a special case, the proof would be simpler without it. That is, I suggest T_n to be defined on the half-closed interval [0,1) only. The count of fixed points will decrease by 1 but the proof should withstand it. Am i too optimistic ? --FvdP 18:14, 12 June 2007 (UTC)
replies: text: I agree with you; the inclusion of 1 is an ugliness there doesn't seem any reason for. -Chinju (talk) 05:26, 24 February 2013 (UTC)
replies: text:  Although I realize now that this makes the equivalence to the necklace-counting proof clearer! -Chinju (talk) 07:40, 27 February 2013 (UTC)
thread_title:  dynamical system proof : do we need T_n(1) ? 

message: The article states:
"We can prove the cancellation law easily using Euclid's lemma, which states that if a prime p divides a product rs (where r and s are integers), then either p divides r or p divides s."
But this is a questionable "proof", since most developments of number theory define the concept of prime in a ring by precisely this property:  "An element p is prime if whenever p divides a product rs, then p divides r and/or p divides s."
For this reason, it would probably be better to use a different means of completing this proof.Daqu (talk) 00:24, 31 December 2007 (UTC)
thread_title: Questionable step

message: I am not a mathematician.  I just read the first proof out of curiosity.  I followed everything except where it says "One can use the following rule to work out how many friends a given string S has: If S is built up of several copies of the string T, and T cannot itself be broken down further into repeating strings, then the number of friends of S (including S itself) is equal to the length of T."  There is no argument given why this rule always works, and I cannot prove to my satisfaction that it does (although I trust that it does).  —Preceding unsigned comment added by 2.120.138.129 (talk) 09:19, 22 March 2011 (UTC)
thread_title:  gap in first proof 

message: I don't understand the last proof in this article. Why is the sum in the first line divisible by p? KarlFrei (talk) 13:31, 24 June 2022 (UTC)
thread_title:  Proof by geometric series