## Re: Prime chains x-->Ax+B

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• ... For that A does not make sense. If you specify only A, then I may always choose a B such that /no/ proof exists. Hence your maximal length is
Message 1 of 143 , Dec 1, 2010
"mikeoakes2" <mikeoakes2@...> wrote:

> Definition: A "maximal power chain" is a power chain with
> integers (A,B) for which there is a proof that no chain
> of greater length exists for that A.

"For that A" does not make sense. If you specify only A,
then I may always choose a B such that /no/ proof exists.
Hence your "maximal" length is unbounded, "for that A".
However, no worry: we do not need the word "maximal".

> Definition: L2(A) = (largest prime divisor of (A-1)) - 1.
> Conjecture: there are only 4 maximal power chains of
> length >= L2(A)+2.

So let's make that clear and self contained:

! Mike Oakes conjectures that for chains x-->Ax+B, with
! A > 2 and B /coprime/ to the /largest/ prime divisor M|A-1,
! it is possible to find a chain of M+1 increasing primes
! in precisely 4 cases.

This erases historical confusion and concentrates on what you
actually studied, with /coprime/ and /largest/ spelled out as
the central points of a (now) coherent conjecture.

> \$\$lots for anyone who can find a 5th one (not:-)

How many zlotys are you offering :-?

David
• ... Suppose that we want to start with a square and get a square. Then we must solve the Diophantine equation y^2 = a*x^2 + b For any pair (a,b), Dario will
Message 143 of 143 , Jan 7 5:30 AM