User talk:Ericswebber

Welcome!
Hello, Ericswebber, and welcome to Wikipedia! Thanks for your contributions; I hope you like it here and decide to stay. We're glad to have you in our community! Here are a few good links for newcomers:


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Happy editing!

-- Sango  123  20:38, July 14, 2005 (UTC)

P.S. Feel free to leave a message on my talk page. :)

Perfect number article
Hi, Ericswebber. Here is the change that User:Jitse Niesen made to your contributions. As you can see, this editor hasn't removed your work, he has only reformatted it and moved it further down the page; however, he has removed the source you provided (ericswebber@gmail.com). Please feel free to contribute to the article and all others in whichever way you choose to, but also note that your work will most likely be edited and redistributed. See also: Ownership of articles and Copyrights.

If I have failed to answer your questions, please let me know; I will try my best to help.

Best regards and happy editing,

Sango 123  23:42, July 14, 2005 (UTC)


 * Hello Ericswebber. I realize that I should have explained to you what I had been doing, as it can be quite confusing to see the material you added disappear; sorry for that. There are a lot of people around, and most edits will be checked (and perhaps even rechecked) before the end of the day. I tried to integrate the material you added in the rest of the article. Of course, if you don't like my changes, you can edit the article again and undo the parts that you do not like.
 * You asked me whether I had heard about the new material you added. The answer is "no," at least not as far as I remember. However, two of the fact were immediately obvious to me (that they are sums of the first so many positive numbers and that the reciprocals of the factors add up to 2); I have been doing mathematics since 1993, first as a student and now I'm employed at university, so I have some experience. I also read the MathWorld article which is referenced at the bottom of the Perfect number article, which lists all the things that you added, so that I could feel confident that they are true.
 * I will try to explain the following fragment:
 * "Since any even perfect number has the form 2n&minus;1(2n &minus; 1), it is the sum of all natural numbers up to 2n &minus; 1. This follows from the general formula stating that the sum of the first m positive integers equals (m2 + m)/2."
 * I assume you know the formula of the first m positive integers, since you wrote this yourself in the article. Now, if you replace m by 2n &minus; 1, you get that the sum of the first 2n &minus; 1 positive integers is
 * $$ \frac{(2^n-1)^2 + (2^n-1)}{2}. $$
 * You now need some agility with handling formulas. I do not know how much mathematics you have been exposed to, so I might go too fast, but the steps are like this:
 * $$ \frac{(2^n-1)^2 + (2^n-1)}{2} $$
 * $$ = \frac{(2^n)^2 - 2\cdot2^n + 1 + 2^n - 1}{2} $$
 * $$ = \frac{2^{2n} - 2^n}{2} $$
 * $$ = 2^{2n-1} - 2^{n-1} \, $$
 * $$ = 2^{n-1}(2^n - 1). \, $$
 * The last expression is exactly the form in which we know that all (even) perfect numbers can be put.
 * I hope this clarifies things a bit. Feel free to ask me for more details if necessary.
 * All the best, Jitse Niesen (talk) 21:20, 15 July 2005 (UTC)