User talk:Divineprime

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[edit] Fibonacci number

Welcome to Wikipedia. I have removed the new section that you contributed to the Fibonacci number article because it was badly written and very unclear. New contributions are welcome, but they must conform to the high standard of writing that is shown in most Wikipedia articles. I have listed some specific problems with you contribution on the article's talk page, at Talk:Fibonacci number. Please can you correct the errors in the section, or work with someone else to improve it, before you try to re-insert it. Gandalf61 13:27, 5 April 2006 (UTC)

I see you have re-written your contribution and added it to the Fibonacci prime page instead. Your re-write is a lot clearer, and I think I can now understand what you are trying to say. However, I now have two further questions:

1. How do you justify your statment GCD(F(n), F(m)) = F(GCD(n,m)). This is not an obvious result - it certainly does not follow from the fact that F(pq) is a multiple of F(p) and of F(q). Do you have a reference for this result ?
2. What is "Charmichael's theorem" ? Are you sure you have spelled this correctly ?

Your contribution is now only about composite Fibonacci numbers, so I don't think it belongs on the Fibonacci prime page. If we can tidy up your contribution a bit more, I think we should move it back to the Fibonacci number page. Gandalf61 10:29, 10 April 2006 (UTC)

Saw your further comments on Talk:Fibonacci number. Your made some remarks of a personal nature. There is a Wikipedia policy Wikipedia:No personal attacks which says, in part, there is no excuse for personal attacks on other contributors. I suggest you read this policy.

Regarding your edits to Fibonacci prime, can you please clarify whether Carmichael's theorem is the result GCD(F(n), F(m)) = F(GCD(n,m)), or is it something else ? The external link that you have titled "Greatest common divisor of two Fibonacci numbers" does not actually clarify this - it simply states this result, without reference or proof. Gandalf61 08:28, 11 April 2006 (UTC)

Okay, I did a Google search and found Carmichael's theorem, with references. Still not clear where you get the result GCD(F(n), F(m)) = F(GCD(n,m)) from - can you provide a link to a proof of this result ? Gandalf61 11:06, 11 April 2006 (UTC)

I removed your first contribution because it was badly written and unclear. It also made an incorrect assertion about the likelihood of a Fibonacci number with prime index being itself a prime. Numerical evidence indicates that a large majority of Fibonacci numbers with prime index are in fact composite - Fibonacci primes are very rare. Your re-write is clearer, and has dropped the incorrect assertion - but it could be made better still. As you are new to Wikipedia, I am offering to work with you to improve your contribution. If you do not want to do this, then I will tidy it up myself. I also think it should be moved from Fibonacci prime back to Fibonacci number, as it says nothing about Fibonacci primes. Gandalf61 14:22, 11 April 2006 (UTC)

Okay, here is how I see it; Go ask Chris Caldwell at that link if you are worried, or want to expound. It's not your job to eliminate information in the way you want. Previously the Fibonacci prime sections stated: "It seems likely that there are infinitely many Fibonacci primes, but this has yet to be proven.". Well why is it likely then? This is a stupid statement without any explanation or link. Am I right? Yes I am correct. So I wanted to add useful information about the limitation of it's factors, for it to make sense.

The article reads very well now actually. The first part eliminates the factors that cannot be, so factors that do occur will be "primitive". It does not say that there will be a factor. The second part (Carmichael) verifies that there must be at least one factor(itself prime), or a product of primitive primes. You have to prove that Carmichael's theorem is wrong or incorrectly stated. Good luck pal.

Now I have read this a third time and it is even clearer, how wrong you are. The assertion was not meant in the way you think it was. Look at you trying to school me, on the density of Fibonacci primes...When I am indeed schooling you, the absent minded. It shall stay right here, in the Fibonacci primes section. You may adjust it, and I will watch it for unacceptably drastic changes.

I've found a reference for GCD(F(n), F(m)) = F(GCD(n,m)); Paulo Ribenboim states it in My Numbers, My Friends, although he does not give a proof. I have added this reference to the Fibonacci prime page. It would be good to see a proof, if you know of one. And I still don't see what either this result or Carmichael's theorem tells us about the density of Fibonacci primes. Gandalf61 09:51, 12 April 2006 (UTC)

You are obviously still not understanding it correctly. The arbitrary examples are complete gibberish. This is completley useless filler to the reader.

Mathworld shows the GCD rule TWICE chap! Sections 89 and 102 (Michael 1964; Honsberger 1985, pp. 131-132).

Ron knott had wrote, Every k-th Fibonacci number is a multiple of F(k) or, expressed mathematically, F(nk) is a multiple of F(k) for all values of n and k from 1 up.

A Primer For the Fibonacci Numbers: Part IX M Bicknell and V E Hoggatt Jr in The Fibonacci Quarterly Vol 9 (1971) pages 529 

- 536 has several proofs that F(k) always divides exactly into F(nk): using the Binet Formula; by mathematical induction and

using generating functions. End quote

So by induction the the greatest common divisor follows from this expression. This is how I came about the obvious answer in my head, and is why you do not understand thus far. Two consecutive Fibonacci numbers are relatively prime right?

What this tells us about the density of Fiboancci primes is that: A. They have a well defined form and properties, for which should be properly expressed, by placing p into the GCD identity.(that's original by me) B. The GCD rule shows that repeat factors can be eliminated, but it does not specify that a special factor must even occur at all. By eliminating possible factors, fewer unique combinations (products) are left. C. Carmichael's theorem implies that there are an infinite number of Fibonacci numbers of the form Fp, that also have just one (at least one) prime special factor. Otherwise it would say something like (at least one...two...x) to be a complete statement, that implies an infinite number of

consecutively composite Fp. The implication of likelihood is quite the opposite! If there were a finite number of prime Fp, Carmichael's statement would be worded incorrectly or incompletely. This is not a proof, but a likelihood of truth.

You still have not replied to the contradiction in your arguement about the "likely". Why does the Fibonacci number page state that it is likely without reason? You attacked me personally when you contradict yourself, by removing my likely explanation. Common factors, on the Fibonacci number page is complete gibberish under your strict terms upon me. I cannot understand why this is okay, and my definition is not. Explain yourself and bias nature please.

quote Any two consecutive Fibonacci numbers are relatively prime. Suppose that Fn and Fn+1 have a common factor g. Then Fn+1 − Fn = Fn−1 similarly. Thus by induction, all preceding Fibonacci number must be a multiple of g. But F1 = 1, so g = 1. end quote

What is unclear about it? It seems to me a perfectly correct proof, by descending induction, albeit exceedingly simple.

−Woodstone 21:07, 11 April 2006 (UTC) Retrieved from "http://en.wikipedia.org/wiki/Talk:Fibonacci_number"

This is much less clear. I get it vaguely, and it really says the same thing, but this is much worse then my additions.

Ron knott mentions this proof by Tm E Ace, for the relative primality of two consecutive Fib. http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibmaths.html#relprime This is much clearer than the current proof given for common factors.

Section 89 of mathworld also states: For n=>3 Fn divides Fm iff n divides m. (Wells 1986, p. 65).

[edit] Talk pages

Divineprime, if you want to leave personal messages or comments for myself or any other Wikipedia user, you can do so at the user's talk page - mine is here. Article talk pages like Talk:Fibonacci number are only intended for discussion about the relevant article. I suggest you read this tutorial on talk pages, which contains a lot of useful information - including instructions on how to sign your comments, which is a big help to other people who may be following a discussion. Gandalf61 10:38, 13 April 2006 (UTC)