Re: JSH: Finally! They're caught.

On Mar 29, 12:06 pm, JSH <jst...@xxxxxxxxx> wrote:
On Mar 29, 10:27 am, Enrico <ungerne...@xxxxxxx> wrote:





On Mar 29, 10:48 am, JSH <jst...@xxxxxxxxx> wrote:

Now readers can finally see clearly what I've had to face for years:
some of those among you are anti-knowledge.

It has been so frustrating watching these people get away with it for
years.  And now the result that proves my point by how they react to
it.

Notice, they have all the warnings too!!!  Yet they still are fighting
it.  That is telling.

It is such a beautiful mathematical result too.  A family of three
equations connected to Pell's Equation, where primes come in as well
with D being prime, where they are EASIER to solve.

That creates a story where none of the old lies and manipulating
techniques they use can hold.

But some of them are trying anyway which is an expression of contempt
for you.

I don't think they see most of you as being anything but their tools.

They've ruled you for so long that they have no respect for your
intelligence.

Yup.  They've RULED you.  That's why they fight so hard.

You have been slaves in mind, if not in body.

You have been servants to a class of people who have nothing but
contempt for you.

James Harris

=======================================================================

It is such a beautiful mathematical result too.  A family of three
equations connected to Pell's Equation, where primes come in as well
with D being prime, where they are EASIER to solve.

Given:  29718^2 - 61*3805^2 = -1

Show me how your equations are used to find
a solution to the more difficult:

X^2 -61*Y^2 = 1

                          Enrico

The equation is:

x = 2Dk^2 - 1 and x = 2j^2 + 1

so x = 1766319049.

I'm more curious though about how long it takes to solve for the
negative Pell's Equation using continued fractions versus Pell's
Equation.

That is coming up as a research question.

James Harris- Hide quoted text -

- Show quoted text -

===================================================================

Ah. So it really does work - transforming a relatively easy
solution into the solution of a difficult one.

The reason I asked about D=61 was that it was a challenge
problem posed by Fermat in the mid 1600's.

I don't find any references in the history to someone
easily picking off the solution - It would have been
noteworthy. (I only looked at one site:)

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Pell.html


Enrico


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