ON:
>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).
>
>So, the upshot is that Davis' criterion for determining whether a Mersenne
>(or in fact any other odd) number is prime amounts to determining whether
>the number has an odd factor > 1.
I mentioned that this was true for all N if F is an odd factor,
it's a bit more complicated, it is only true for N even
if F is an odd factor and F is small enough.
This because we can't use negative numbers.
For example 12 = 3 + 4 + 5 (F=3, Q=4) works and
70 = 7+8+9+10+11+12+13 (F=7, Q=10),
but it fails for 14 because the only odd factor F=7 gives Q=2
and Q < D.
Sorry for that
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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