Talk:Cubic reciprocity

message: I strongly suspect that
:\alpha^{(P-1)/3} \equiv \left(\frac{\alpha}{\pi}\right)_3
should be replaced by 
:\alpha^{(P-1)/3} \equiv \left(\frac{\alpha}{\pi}\right)_3 \mod \pi
which would be somewhat analogous to Euler's criterion for the Legendre symbol. DRLB 18:45, 24 October 2006 (UTC)
replies: text: Yes indeed, fixed now: thanks.  Richard Pinch 06:26, 27 October 2006 (UTC)
thread_title:  Suspected error 

message: In the text it is written "...cubic reciprocity is most naturally expressed...". Is there some other definitions, since it seems I need one "not naturally expressed". Vavlap (talk) 01:25, 16 April 2008 (UTC)
replies: text: I agree that the current presentation is too abrupt. In a more gentle version the notion of "cubic residue" should be defined separately, and there should be a better explanation of the term "reciprocity" in this context. The lede mentions cubic equations, a term that does not recur in the article, making this only more mysterious.  --Lambiam 04:49, 24 April 2008 (UTC)
thread_title:  Natural? Maybe. Understandable? Less so 

message: I rewrote this based on my article on quartic reciprocity. I think the abruptness has been removed. I gave it a B+ rating. Virginia-American (talk) 23:15, 5 December 2008 (UTC)
thread_title: Rewrite

message: This article does not clearly state an algorithm to find the cubic residue to satisfy x^3=p mod q. Is there any algorithm available? Jackzhp (talk) 15:45, 20 January 2018 (UTC)
thread_title: algorithm to find the cubic residue

message: The first sentence in the section History is as follows:
"Sometime before 1748 Euler made the first conjectures about the cubic residuacity of small integers, but they were not published until 1849, after his death."
There is nothing wrong with using the word "residuacity" except for the fact that 99.9999% of readers will have no idea what it means.
(To make matters worse, there is also no explanation of its meaning, and no link to any explanation. But please do not think that a link to an explanation would have been a good idea: It would not be.)
Please remember that writing in Wikipedia is for the purpose of making things clear to readers. 2601:200:C000:1A0:D02F:D749:A7D7:6091 (talk) 20:13, 21 June 2021 (UTC)
thread_title:  There's nothing wrong with using the word "residuacity" except 

message: The section Facts and terminology contains this passage:
"\Z[\omega] is a unique factorization domain. The primes fall into three classes:Ireland & Rosen Prop 9.1.4
* 3 is a special case: 
:: 3 = -\omega^2 (1-\omega)^2."
Is the writer truly unaware that the word "primes" could refer to the primes of the unique factorization domain \Z[\omega] that was just mentioned??? 2601:200:C000:1A0:D02F:D749:A7D7:6091 (talk) 20:22, 21 June 2021 (UTC)
thread_title:  Sloppy writing 

message: I think that there is no generalized way to calculate whether m is n-th power residue mod d (i.e. x^n == m mod d has solutions) for n = 5, 7, etc. i.e. n is not divisor of 24, since there is no algebraic solution for a generalized algebraic equation with degree n for n>4, however, for n=6 it is only needed to test n=2 and n=3, thus there is still a way, and there is an article of octic reciprocity, thus for n=8 there is also a way, therefore, I think that there is a way if and only if n is divisor of 24 (possibly 48 instead of 24). ——220.132.54.182 (talk) 09:09, 29 December 2021 (UTC)
thread_title:  I think that there is no generalized way to calculate whether m is n-th power residue mod d (i.e. x^n == m mod d has solutions) for n = 3, 4 but not 5, 7