> From: "Griffith, Shaun" <[EMAIL PROTECTED]>
> To: "'[EMAIL PROTECTED]'" <[EMAIL PROTECTED]>
> Subject: RE: Mersenne Digest V1 #492 (spin structures)
> Date: Thu, 7 Jan 1999 11:03:40 -0600
> MIME-Version: 1.0
>
> Benny van Houdt wrote:
> >Ernst W. Mayer wrote:
>
> >>If an odd number N has a factor F < N, then N can be expressed as the sum
> of F
> >>consecutive integers, as follows: Let Q = N/F and D = (F-1)/2, then
> >>
> >>N = (Q-D) + (Q-D+1) + ... + Q + ... + (Q+D-1) + (Q+D).
>
> >I guess, its F that has to be odd and not N.
>
> >Benny.
>
> Since N is odd, F must be odd, as odd numbers cannot have 2 as a factor.
> [You remember - Even*Any=Even, Odd*Odd=Odd?]
>
> Since F is odd, D=(F-1)/2 is also odd.
>
> But you've got one on me if you can wade through the rest of that with any
> sanity left :-)
>
> -Shaun
>
All I wanted to state is that this property is valid for any N (not
only odd ones) as long as F is an odd factor of N.
BTY D can be even ( 2=(5-1)/2 for example ).
Benny
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Benny Van Houdt,
University of Antwerp
Dept. Math. and Computer Science
PATS - Performance Analysis of Telecommunication
Systems Research Group
Universiteitsplein, 1
B-2610 Antwerp
Belgium
email: [EMAIL PROTECTED]
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