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• Wednesday, March 15, 2006 8:11 AM [GMT+1=CET], ... Thanks to Phil and Jose, I was slightly obtuse ... But, someone could tell us how to prove that it must be p
Message 1 of 23 , Mar 19, 2006
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
>
> 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)?