Re: JSH: Learning from the negative Pell's Equation

You have been shown this before.  You keep denying it.  Here it is
from the Wikipedia article on Brahmagupta:

 "Unfortunately, Brahmagupta was not able to apply his solution
  uniformly for all possible values of N, rather he was only able
  to show that if x^2 - Ny^2 = k has an integral solution for
  k = +/- 1, +/-2, +/- 4 then x^2 - Ny^2 = 1 has a solution."

Brahmagupta did not know the continued fraction solution, but
it is absolutely clear from the above that he "only" knew what you
claim as a great discovery.  By modern standards with modern
notation, Brahmagupta's result is a triviality.  So is yours,
and clearly it is well known.

Marcus.

For me the chilling proof that math society itself willfully lies can
be seen with some really trivial algebra, Pell's Equation and the
negative Pell's Equation which is why I keep mentioning it, as I can
beat up on math society worldwide with this result indefinitely.

Given ANY set of non-zero integer solutions to the negative Pell's
equation

j^2 - Dk^2 = -1

you will ALWAYS have a solution to Pell's Equation

x^2 - Dy^2 = 1

from x = 2j^2 + 1.

That is a mathematical absolute.  Now go try to find it in a
contemporary mathematical textbook.

What I like about this result is how clearly it shows the political
nature of the modern field of number theory.

Number theorists, quite simply, lie.  I dare them to keep ignoring
this result!  I like beating up on them.

James Harris