Talk:Lucas sequence

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[edit] Condition on P and Q

To clear up any confusion - the correct condition on P and Q is

as given by Paulo Ribenboim in My Numbers, My Friends. MathWorld incorrectly has the condition

P² − 4Q > 0

but all the relations work equally well if P²-4Q is negative. Gandalf61 08:41, 5 May 2006 (UTC)

[edit] Clarification of opening

Lucas sequences were first studied by French mathematician Edouard Lucas.

Is this really true? In general, the sequences of convergents in simple continued fraction expansions of quadratic surds contain embedded Lucas sequences. I understand that Lucas generalized the notion, and wrote quite a few papers about his generalized sequences. But Joseph Louis Lagrange (d. 1813) solved the general problem posed by Pell's equation, and Euler studied the convergents of continued fractions long before Lagrange did, so I think this sentence is stretching the truth, at a minimum. DavidCBryant 23:09, 9 December 2006 (UTC)

Changed "first studied by" to "named after". Gandalf61 12:21, 10 December 2006 (UTC)

Thanks! Say, I noticed one other thing. Some of the equations in this article appear in a big font, and others are much smaller. (I'm talking about separate lines produced by a pair of <math></math> tags.) Is that intentional? Would it be OK if I fix them to all display in the larger font? DavidCBryant 14:09, 10 December 2006 (UTC)

Not intentional AFAIK, so feel free to fix ! Gandalf61 17:32, 10 December 2006 (UTC)

[edit] Comments on proposed merger

I disagree with the proposed merger of Lucas number into Lucas sequence. Lucas sequences encompass not just Lucas numbers but also Fibonacci numbers, Pell numbers, and in fact any sequence defined by a linear recurrence relation with a quadratic characteristic equation. Making Lucas numbers a special case by merging them into the Lucas sequence article would be anomalous and misleading. Gandalf61 09:40, 21 January 2007 (UTC)

In the german Wikipedia Lucas sequence and Lucas number are only in one article, because they have no different names in german. Both are Lucas-Folgen.

I disagree a merge of Lucas number and Lucas sequence too, because they are different, and have different names.

If someone would like to merge Lucas number to Fibonacci number, i would understand, and accept, because they are twins. --Arbol01 11:17, 21 January 2007 (UTC)

Do not merge the articles. Lucas sequences have wide application in cryptography, primality testing, etc. Lucas numbers are a special instance of a Lucas sequence; they're historically notable in their own right. DavidCBryant 12:39, 21 January 2007 (UTC)

I'm against a merger and agree with the above arguments. Lucas numbers have a similar name but don't have more reason to be in Lucas sequence than other instances of Lucas sequences with their own article. PrimeHunter 18:36, 21 January 2007 (UTC)

Not a problem, this is why I only suggested it. Arbol01: There are certain users who have a problem with Lucas numbers on the Fibonacci numbers page. It just seemed to me that as Fibonacci sequence redirects to Fibonacci number that Lucas number and Lucas sequence should be merged. I see that since I proposed the merger that a link has been added from Lucas number to Lucas sequence. I will remove the proposal. Danielklein 00:57, 24 January 2007 (UTC)

I think Fibonacci number is too long for details about Lucas numbers and other generalizations. If Lucas number should be merged anywhere (I don't support that), then I would prefer Generalizations of Fibonacci numbers (which needs some editing in the Lucas numbers section). PrimeHunter 13:57, 24 January 2007 (UTC)