Mathematicians Crack a Simple but Stubborn Class of Equations [Pell Equations]

Quanta Magazine ^ | August 10, 2022 | Jordana Cepelewicz

[BobL]

The problem looks a bit gay.

[ProtectOurFreedom]

The solution to BiXiden Inflation can only be found in the imaginary mathematical realm...

[ViLaLuz]

All mah integers.

[ViLaLuz]

I hope that the math team included a black, a hispanic, an indigenous person, a gay, a lesbian and a trans person.

Otherwise the results cannot be considered “knowledge” but must instead be treated as heretical thought and banned!
...................

Good little CRT not-sees.

[CapnJack]

“which can be written as x2 – dy2 = 1.

how about x=2, d=3, y=1?

I must be missing something.”

Exactly ... there has to be some trick to it.

[BenLurkin]

[ckilmer]

I don’t understand any of it. Don’t have the wattage/brain power for that kind of thought.

What I do notice is that the rate at which mathematicians are finding solutions to ancient mathematical puzzles —has been accelerating in recent decades.

Likely because computers give them power tools for the first time.

[Red Badger]

If they can be solved, and the Mell equations can be solved, a lot of things will fall into place pell mell. Yeah, my heart wasn't in that one.

You be SMOKIN'!...................

[Mr. K]

Heh heh... I see what you did there

:)

[SunkenCiv]

Glad I’m not the butt of any jokes...

[Red Badger]

You don’t make an ash of yourself...................

[RinaseaofDs]

LOL, you’re BRILLIANT!!

[SunkenCiv]

I’ll tray.

[Scrambler Bob]

“which can be written as x2 – dy2 = 1.

how about x=2, d=3, y=1?

I must be missing something.”

Exactly ... there has to be some trick to it.
= = =

Zero is an integer.

For d=0, x=1 for all values of y.

Yeah, I’m not getting something. I think they want solutions for all values of d. Or a general solution of that.

Just fooling around

x2 = 1 + dy2

so, for x=5
25 = 1+ 6 * 2*2

And probably a bunch more simple ones like that.

I guess the problem is trying all the integers from 0 to infinity. That would take a while. I need a Govt. grant for only $1 per integer (from 0 to infinity). That is chicken feed in today’s Govt. budget.

[Scrambler Bob]

In fact, I’ll only charge $0.00000000000001 per integer from 0 to infinity.