> From: Steinar H. Gunderson [mailto:[EMAIL PROTECTED]]
> On Tue, Jun 22, 1999 at 06:56:42AM +0100, Brian J. Beesley wrote:
> >There is another constraint - 2kp+1 must be congruent to 1 or 7
> >modulo 8.
>
> Here comes something that has been confused me for a long time. Isn't
> 1 modulo 8 = 1? You are always talking about `1 modulo something'.
> My definition of `modulo' (a mod b is the remainder of a/b) gives:
>
> 0 mod 4 = 0
> 1 mod 4 = 1
> 2 mod 4 = 2
> 3 mod 4 = 3
> 4 mod 4 = 0
> 5 mod 4 = 1
>
> etc., and by this follows that 1 mod x = 1 (at least for x >= 1). But
> it looks like I've missed something important...
You are missing the implied parentheses. You seem to be wrongly
interpreting the expression as (2kp) + (1 modulo 8). Interpret it as
(2kp+1) modulo 8 and it might make more sense.
For example, if p = 5, then:
2*1*5+1 = 11 == 3 mod 8
2*2*5+1 = 21 == 5 mod 8
2*3*5+1 = 31 == 7 mod 8
2*4*5+1 = 41 == 1 mod 8
2*5*5+1 = 51 == 3 mod 8
and so on.
Paul
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