Floretions and Re: Dan's Triangular numbers / Primes post

[Creighton Dement]

Thanks very much to you both (Graeme McRae and Thomas Baruchel)! 

On another note: 
I have never heard anyone complain directly to me that I post too much
about the floretions (apparently, some of you are very patient). In
fact, I have only heard other mathematician's nice comments about them
over the last year (there have been times when I lost the motivation to
work systematically- it was then that I seriously considered collecting
all these comments and hanging them up somewhere on my wall at home just
to keep me going). 

That got me to thinking... I toot my own horn too much. Most of you
probably work in research departments where you come into contact with
many other mathematicians during the day. I work as an English teacher
during the day and as a hobby mathematician at night / weekends
(currently, I am also still enrolled as a student at my university). 
That leads me to ask many questions that others probably wouldn't ask. 
Therefore, I apologize if I've gotten on anyones nerves. Happily, I can
say that a professor has set aside some time for me during this semester
- I just need to call and make an appointment. 

Yours Sincerely, 
Creighton 


 
 
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> Date: Wed, 19 Oct 2005 17:25:28 +0200
> Subject: Re: Dan's Triangular numbers / Primes post
> From: "Graeme McRae" <g_m at mcraefamily.com>
> To: <seqfan at ext.jussieu.fr>, "Creighton Dement" <crowdog at crowdog.de>

> This question is very similar to the question "why can a prime number,
> p, be written as the difference of two squares in only one way?"
> 
> To answer that question, you need to factor the difference of two
> squares, and see that if the product is prime, then one of the factors
> must be 1.
> 
> In the same way, the difference between the nth and the mth triangle
> number is
> 
> (m)(m+1)/2 - (n)(n+1)/2, which equals
> 
> (m-n)(m+n+1)/2
> 
> If this product is a prime, p, then either m-n=2 and m+n+1=p, or else
> m-n=1 and m+n+1=2p.  No other pair of numbers, m,n, will result in
> this product being equal to p.
> 
> --Graeme
> 
> 
> ----- Original Message -----
> From: "Creighton Dement" <crowdog at crowdog.de>
> To: <seqfan at ext.jussieu.fr>
> Sent: Tuesday, October 18, 2005 3:09 PM
> Subject: Dan's Triangular numbers / Primes post
> 
> 
> 
> > Dear Seqfans,
> > 
> > I would like to post a link to a thread started by someone else on
> > sci.math that I find interesting. Perhaps some of the experts from
> > the seqfan list can be helpful to the seemingly very polite "Dan".
> > 
> > http://mathforum.org/kb/thread.jspa?threadID=1267639&tstart=0 
> > 
> > 
> > 
> 
>