Talk:Cohn's irreducibility criterion

message: Provides no context, but I think it's obvious that it's maths-related. Listed at Wikipedia:Missing_science_topics/Maths1, doesn't really make sense to go speedying articles which have been requested. --Cornflake pirate 11:33, 16 July 2006 (UTC)
thread_title: Speedy deletion

message: You are NOT using appropriate counter examples.  You are violating the basic conditions of Cohn's criterion.  The coefficients have to be integers between 0 and 9, inclusive. You are using integer coefficients between -9 and +9 inclusive.  The original statement of the theorem uses the addition operator between polynomial terms, and states that the coefficients must be positive integers.
I originally came to this talk page today to ask if the coefficients could be negative.  I do not know for sure that they cannot be in theory. But it is not stated or proven on this page; you, however, are just using this as such like its second nature.
64.134.140.53 (talk) 00:32, 29 September 2012 (UTC)
thread_title:  Response 

message: I agree with Gandalf's new wording.  This is just a note to clarify which mathematician first gave each version of the theorem.  (This is more detail than is needed in the article proper).
Library searches don't come up with any origin of Cohn's theorem except its appearance in Polya and Szego's book, published in 1925. (I looked it up in the original). They assert Cohn's theorem specifically for base 10 (vol. 2 page 137).  They also include the condition that the leading digit be greater than one.  I don't think it hurts to leave that condition out because the corresponding polynomial than just starts with the first non-zero digit.  They do of course have the condition that all the coefficients range between 0 and 9 inclusive.
The unmodified generalization of Cohn's original rule to bases other than 10 was first given by Brillhart et al 1981. Polya and Szego (1925) have their own generalization but it has many side conditions (on the locations of the roots, for instance) so it fails to be completely Cohn-ian.
It's clear from context that this A. Cohn must be Arthur Cohn, a student of Issai Schur who got his PhD in 1921.  He is listed in the Mathematics Genealogy Project. EdJohnston 20:52, 30 August 2006 (UTC)
thread_title:  Found the original source 

message: Pólya, G., G. Szegö (1925). Aufgaben und Lehrsätze aus der Analysis, vol. 2. Springer, Berlin.
I think the authors are George Pólya and Gábor Szegő, however only the former article mentions the book, as Problems and Theorems in Analysis.
Aufgaben Und Lehrsatze Aus Der Analysis on Amazon.com shows publication as Dover (1945) and Springer; 4 edition (July 1, 1970).   shows Springer; 4 edition (July 1, 1971).  Is it ok to use the ISBN of the incorrect edition?  John Vandenberg 12:51, 27 November 2006 (UTC)
replies: text: I think it would be fine to provide the ISBN of a recent edition in English. In the present article, some results are identified by page number, so it would help to include the 1925 edition in the reference list. The 1925 is the only one I have actually seen.  For this purpose, and if the book is too early to have an ISBN, an OCLC is ideal, since it specifies a particular  edition. No harm in including a more recent edition as well. EdJohnston 00:58, 28 November 2006 (UTC)
thread_title:  Sources 

message: "The converse of this criterion is that, if p is an irreducible polynomial with integer coefficients that have greatest common divisor 1, then there exists a base such that the coefficients of p form the representation of a prime number in that base; this is the Bunyakovsky conjecture and its truth or falsity remains an open question."
If a polynomial with integer coefficients is irreducible, then its coefficients do have gcd 1. The author might have meant "whose values on integers have gcd 1", or "whose coordinates in the canonical basis of integer-valued polynomials are coprime" (otherwise his conjecture is obviously false), but then, the (unsourced) conjecture seems to me much weaker (hence − maybe − solved ?) than Bunyakovsky's. Anne Bauval (talk) 20:54, 2 January 2013 (UTC)
thread_title:  Dubious conjecture 

message: Substituted at 01:53, 5 May 2016 (UTC)
thread_title: Assessment comment