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

Then why didn't you just agree before?

There aren't.

I don't know.

Then cite in modern literature the result that given a solution to the
negative Pell's Equation j^2 - Dk^2 = -1, you always have a solution
to Pell's Equation x^2 - Dy^2 = 1, from x = 2j^2 + 1.

Your insults betray your lack of confidence here.

Then why argue?  Why not just agree that the result follows?

I dare you, just agree.

Given a solution to the negative Pell's Equation j^2 - Dk^2 = -1, you
always have a solution to Pell's Equation x^2 - Dy^2 = 1, from x =
2j^2 + 1.

Agree?

James Harris

But this was not disputed.
You were claiming that there were no previous references
or clear references to this in the modern mathematical literature.
Why else would I give the Carmicahel reference ?

Clearly Carmicahel disproves your claim and you have shown
youself to be a fool because,without an example, you could not
understand that Carmicheal includes and goes beyond your statement
above.

On May 16, 11:22 am, marcus_bruck...@yahoo.com wrote:

Good.  Progress.

Then you agree that given a solution 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?

Simple question.  Only requires a simple answer.

James Harris

Sure.  Brahmagupta's identity, from the Wikipedia article,
immediately implies that if (x, y) is a solution to

       u^2 - Dv^2 = =/-1,

then (x^2 + Dy^2, 2xy) is a solution to

       u^2 - Dv^2 = +1.

Hence, starting with your example: (2, 1) is a solution
to

       u^2 - 5v^2 = -1,

therefore (2^2 + 5*1^2, 2*2*1) = (9, 4) is a solution to

       u^2 - 5v^2 = 1.

Period.  Trivial application of Brahmagupta's well-known
result.

Marcus.

On May 16, 10:45 am, marcus_bruck...@yahoo.com wrote:

Then work an example relying on what you quoted.

I'll work an example based on what I gave:

2^2 - 5*1^2 = -1, so x = 2*2^2 + 1 = 9, and 9^2 - 5*4^2 = 1

Note that here D=5.  j=2, and since x= 2j^2 + 1, you have x = 9.

Now YOU work an example.

I hate how some of you babble on in these long-winded replies that are
just straight lies.

WORK AN EXAMPLE based on what you claim.

Do math, not sophistry.

James Harris

 Notice that if you had bothered to read the Wikipedia
article, you would have found Brahmagupta's expressions
which generalize yours.  Nothing is being covered up
here.

 I did not lie at all.  Your result is well-known and well-
explained in the literature from 1500 years ago.

 Ergo, you do not read any references, even those that are
most easily accessible.

 Oh sure.  Telling the truth about this is a political act.

 Are we now talking about your post, where the objectives are
to obtain recognition for your great genius and to show that
mathematicians lie?  Is that the part that nothing to do with
mathematics?

 Again I'm getting confused.  I would think that your
refusal to read details as in e.g. the Wikipedia article indicates
a disdain for knowledge.  Looks like we are talking about
you and your "darker side", not that of mathematicians.

 Marcus.

On May 16, 8:46 am, marcus_bruck...@yahoo.com wrote:

Readers can simply look at your previous reply in this thread and
contrast it with what I've said, where I'll repeat the math yet again.

Given  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.

Notice I GIVE the solution for x.

The result is fairly trivial but the point here is that with something
not seen in the mainstream literature rather than behave like real
researchers who value knowledge, you and posters like you, lie.

Ergo, you do not value knowledge!  Your intentions in posting must
then be about something else.

In my opinion you post simply to coerce the crowd in a direction of
your choosing, so your postings are political!!!

So what you do in posting has nothing to do with mathematics.

It is all about a darker side in human nature, and a disdain of
knowledge.

James Harris

Cite a reference where someone has lied about this.

Marcus.

On May 15, 5:41 pm, marcus_bruck...@yahoo.com wrote:

That is not the same as, given  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.

Notice I GIVE the solution for x.

Further note that if j is the first solution then x is the first
solution to Pell's Equation.

Nope, it's not a great discovery.

It's completely trivial.  Easily proven.  Probably well-known to
Fermat and Euler.

Lies.

What is remarkable to me is that readers can easily search on the
subject.

I don't claim this result is some great discovery.  It's not.

I simply claim it's an easy way to watch modern number theorists, lie.

James Harris

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