Dan's Triangular numbers / Primes post

[Graeme McRae]

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
>
>
>