Re: [PrimeNumbers] Re: Extending the 10 squares conjecture
- --- jbrennen <jack@...> wrote:
> --- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:Smart method.
> > For n>2, the simultaneous equations:
> > ab+1=x^n
> > ac+1=y^n
> > bc+1=z^n
> > have no solutions.
> Oh, really. I found a solution. :-)
> (a,b,c,x,y,z,n) == (2,171,25326,7,37,163,3)
> To effectively search this, don't vary (a,b,c). Instead choose n,
> then vary (y,x,a). y goes from 3 to LIMIT; x goes from 2
> to y-1; a iterates over the divisors of gcd(x^n-1,y^n-1).
> The solution above takes less than one second to find.
The good Christian should beware of mathematicians, and all those who make
empty prophecies. The danger already exists that the mathematicians have
made a covenant with the devil to darken the spirit and to confine man in
the bonds of Hell. -- Common mistranslation of St. Augustine (354-430)
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