- --- On Fri, 1/27/12, WarrenS <warren.wds@...> wrote:
> > Mod(Mod(1,n)*(l+2),l^2-x*l+1)^(n+1)==2*x+5

Apparenty you are not familiar with one of the linguae francae

>

> --what is Mod(1,n)?

on this list, namely that of Pari/GP. As Pari/GP is portable,

trivially available, and free, it stands out as one of the most

popular languages we use. It's perfect for prototyping.

Packages/source: http://pari.math.u-bordeaux.fr/download.html

Docs: http://pari.math.u-bordeaux.fr/doc.html

The above is the notation it uses to represent elements of a ring

defined by modular reduction.

> (And by the way, do you mind not being a total jerk by using the

You might consider simply using a font that makes different characters

> letter l which is visually almost the same as the number 1?

look, erm, different.

You might also consider moderating your tone. I know from your private

e-mails that you find that hard, but can you please try harder on-list?

You clearly have many intersting mathematical ideas to share, they're

best not clouded by such noise.

Phil - --- In primenumbers@yahoogroups.com, "paulunderwooduk" <paulunderwood@...> wrote:
>

Combining fails with the composite counterexample n=256999 and x=32768, However, I have tested the 1+1+1+2 conjecture up to n<10^7,

>

>

> --- In primenumbers@yahoogroups.com, "paulunderwooduk" <paulunderwood@> wrote:

> >

> > Hi,

> >

> > I have added a Fermat test to make a 1+1+1+2 selfridge test:

> >

> > For N>5, with gcd(6,N)==1, find an integer x:

> > gcd(x^3-x,N)==1

> > kronecker(x^2-4,N)==-1

> >

> > and check:

> > (x+2)^((N-1)/2)==kronecker(x+2,N) (mod N) (Euler)

> > (x-2)^((N-1)/2)==kronecker(x-2,N) (mod N) (Euler)

> > x^(N-1)==1 (mod N) (Fermat)

> > L^(N+1) == 1 (mod N, L^2-x*L+1) (Lucas)

> >

>

> Note: I should say gcd(30,N)==1 because gcd(x^3-x,N)==1 and kronecker(x^2-4,n)==-1.

>

> Re: http://tech.groups.yahoo.com/group/primenumbers/message/24090?l=1

>

> Now consider combining the 2 Euler tests with the Lucas test:

>

> (L*D)^((n+1)/2)==D (mod N, L^2-x*L+1) (D=x^2-4.)

>

> with the restriction kronecker(x+2,N)==-1.

>

> These together with the Fermat test makes for a 1+2-selfridge test.

>

> Can you find a counterexample?

>

> So far the near-refutation from Pinch's carmichael list is:

> N,x,gcd(x^2-1)

> ------------------

> 1909001 884658 1909001

>

> Paul

>

Paul -- restoring symmetry