Re: [PrimeNumbers] Re: Prime chains x-->Ax+B [puzzle 11]
> Puzzle 11: Find a plupluperfect chain of 12, i.e. aThis doesn't fit the 'tuplet' pattern, but would fall to raw 'gensv'.
> (A, B, p) such that A = 1 mod 11, B is coprime to 11,
> and the iteration p[n+1] = A*p[n] + B yields a chain of
> 12 increasing primes, p[n], for n = 1 to 12.
> Comments: Clearly, p = 11 and hence B = 11 - A*p, with
> p = 2, 3, 5 or 7. So this boils down to 4 sub-problems of
> Carmody-scale difficulty (maybe easy for Phil; harder for mere
> mortals like Kevin, Mike, or me). I did not yet find a solution.
Unfortunately the only wrapper around 'gensv' that works currently is
'tuplet', not the raw engine. So I'll have to duck out of this until
2015, when I finally get gensv working again.
- --- In email@example.com,
Kevin Acres <research@...> wrote:
> x=a*x+b either is a square or has a square as a major factor.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 tell us all the solutions: