Talk:Markov number
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To delimit Markov triples, Mathworld uses parentheses
- (1, 1, 1), (1, 1, 2), ...
though a Mathematica command would most likely return
- {{1, 1, 1}, {1, 1, 2}, ...
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)
- Usually, curly brackets denote sets and parentheses denote tuples. In a set, every entry can occur only once, so I'd say it should be parentheses. This is also what [1] uses. -- Jitse Niesen (talk) 22:21, 25 October 2005 (UTC)
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- I've gone ahead and changed the brackets to parentheses. Anton Mravcek 20:38, 27 October 2005 (UTC)
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- It's precisely because of Mathematica that I used curly brackets. I simply copied and pasted the Markov triples. I didn't give it a second thought. Perhaps per analogy to Brown numbers we should use parentheses here. PrimeFan 17:25, 27 October 2005 (UTC)
[edit] Markov primes
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)
[edit] Interesting Preprint
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.
