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

Why Thank You,  Rossum, you have to imagine the putting of the square
peg iin a round hole, the  process hath required a little elbow
grease.--Martin Musatov [P=NP, Just for the taste of it! Diet Coke!]

However, there is a problem...

This equation does not have an integer solution for all non-square D.
What is the solution for D = 7 for example?

Provided you also have a solution to the first equation, which is not
always the case.

Your method does not give an answer for all values of D.  That is also
a mathematical absolute.

You have been given references to Brahmagupta and to a 20th century
textbook.

I think not.  It shows that an inferior method that is incapable of
solving the Pell equation for D = 7 has been discarded in favour of a
superior method, continued fractions, that can solve the Pell equation
for all non-square values of D.  Nothing to do with politics, merely
replacing a less good solution with a better solution.  No need to
look for sinister hidden motives.

rossum

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