Wednesday, March 15, 2006 8:11 AM [GMT+1=CET],

Phil Carmody <

thefatphil@...> escribió:

> --- aldrich617 <aldrich617@...> wrote:

>> I am searching for a way to prove the following Theorem:

>>

>> For any integer 'B', the value 'A' of the equation

>> A = 5B^4 -10B^3 + 20B^2 -15B +11 will have as factors only

>> integers that end in a one, excluding all others.

>>

>> This seems to be true at least up to 10^18. I think that proving

>> it could give us new insights into primality testing,

>> and factoring. Moreover there are similar equations, vast in

>> number, apparently with the same property, that could then probably

>> be verified to be similar threads of pure one. Together these

>> would form an infinite interconnecting web.

>

> Can you tell us how you discovered that polynomial?

> The discriminant is very smooth, being 5^3*11^2, and I suspect that

> that's an essential ingredient to a proof.

>

> It seems that if p== +/-1 mod 10, then your polynomial splits at

> least into 2 quadratics, and if p== +1 mod 10, then at least one of

> those quadratics splits.

>

> This property should be easily explainable, but alas it's late and my

> brain's on holiday. (I wrote this last night, but forgot to send).

Thanks to Phil and Jose, I was slightly obtuse ...

But, someone could tell us how to prove that it must be p = 1 (mod 10)?

Thanks in advance,

Ignacio Larrosa Cañestro

A Coruña (España)

ilarrosa@...