## JSH: Correction to solving binary quadratic Diophantine equations

A poster noted a problem with my original theory that I thought fully covered binary quadratic Diophantine equations as I stupidly assumed coprimeness between x and y given an equation like

x^2 - Dy^2 = F

when F can have a square as a factor.

That poster gave the example of x^2 - 3y^2 = 4, but it turns out in any case with a natural number n, not a unit, given

x^2 - Dy^2 = n^2

where D is a natural number not a unit, solutions must exist as you can reduce to

(x/n)^2 - D(y/n)^2 = 1

so the problem is with square factors, which have to be divided off to force coprimeness which I stupidly assumed.

But other than that the theory is ok. Easy fix. I boringly solved generally solved binary quadratic Diophantine equations.

Turned out it was easy. And now I'm kind of depressed as I'm beginning to wonder about you people.

Am I some kind of genetic freak with super intelligence in a world where the people around me are just too stupid to fully understand me?

If so, why am I so freaking cursed.

I'm living on the planet of the Apes.

The best explanation then for what has been happening is that you all as a group lack the intelligence level necessary for us to communicate meaningfully so it's like if you were trapped on a world of chimpanzees, who happened to be able to talk, barely, but were otherwise, just chimpanzees.

A planet of the apes.

Well that ruins my mood. Looks like all the data is in though.

It's not that you people are actually stupid. It's that I'm some kind of mutant freak of nature in a nightmare of super intelligence trapped on a world where I have no one to talk to like me.

No wonder I'm finally actually going bonkers. I have no hope.