![]() | This article is rated C-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||
|
To delimit Markov triples, Mathworld uses parentheses
though a Mathematica command would most likely return
and I'm guessing that's why PrimeFan chose to do it that way. But it doesn't seem quite right. In the math tags, you have to "escape" any curly brackets you want to show.
So what's the correct way of delimiting Markov triples? With parentheses or with curly brackets? Anton Mravcek 21:57, 25 October 2005 (UTC)
I removed the little bit about Markov primes. Maybe there is some interesting relation between a Markov number that is a prime and its index in the Markov sequence, or some other interesting property of such numbers. But I don't think there are any professional mathematicians researching Markov primes, nor are any large prime discoverers making an effort to identify large Markov primes. Anton Mravcek 20:38, 27 October 2005 (UTC)
Ying Zhang, Congruence and Uniqueness of Certain Markoff Numbers, 2006.
Abstract: By making use of only simple facts about congruence, we first show that every even Markoff number is congruent to 2 modulo 32, and then, generalizing an earlier result of Baragar, establish the uniqueness for those Markoff numbers c where one of 3c - 2 and 3c + 2 is a prime power, 4 times a prime power, or 8 times a prime power.
Can anyone of you tell me how to solve the equation x^2 + y^2 + z^2 = 3xyz 125.234.150.44 08:51, 20 July 2007 (UTC)
The value C = 2.3523418721 quoted in the asymptotic formula for was computed from the value 0.18071704711507 for C^{-2} in Zagier's 1982 paper. Unfortunately that value is inaccurate, most importantly due to an accidentally missing digit, and in fact a more accurate value is used to compute other numbers in that paper. The value should be 0.180717104711806 for C^{-2} and hence C = 2.3523414972 (to 10 places). See OEIS: A261613 for more details. Chris Thompson (talk) 20:08, 20 April 2016 (UTC)
The main page states that the conjecture that was "proved by Greg McShane and Igor Rivin in 1995". I think this is incorrect. That conjecture is equivalent to
(not the same C) where is the number of Markov numbers less than . Don Zagier's 1982 paper proved this with an error term of . The McShane and Rivin paper referenced (which incidentally is most easily accessed as arXiv:math/0005220) improves this to , which is still some way from . In fact such improved estimates of the error term are clearly described in the paper as conjectures, even prompting the authors to remark at the end of the French summary "Nous croyons que la deuxieme conjecture est tres difficile."
In fact the conjecture appears to be still open. The recent paper arXiv:1603.06267 by Gamburd, Magee and Ronan states (Theorem 1) that "The best current result is due to McShane and Rivin", repeating and giving a reference to their other 1995 paper, accessible as arXiv:math/0005222. Chris Thompson (talk) 16:17, 22 April 2016 (UTC)
Sentence: the Markov tree if x is set to 1, 5 and 13, respectively
I think it must be if z is set Jumpow (talk) 19:32, 12 April 2017 (UTC)