Wednesday, April 01, 2009
JSH: Continuing mystery?
So the result I've been trumpeting showing alternates to Pell's Equation are easier is something that should be well-known.
Turns out you don't need any general solution to binary quadratic Diophantine equations.
You can figure it out just from using x^2 - 1 = Dy^2, by noting how D must divide through x+1 and x-1.
The sad story here is I think the answer is about random.
Mathematicians avoid random with prime numbers because random can answer questions supposedly of research interest, like the Twin Primes conjecture and Goldbach's conjecture. (First: True. Second: False.)
THAT to me is the best explanation.
The behavior of primes with Pell's Equation is random, and there is no way to hide that fact with the usual obfuscations used with prime numbers, so the equations I've been so excited about, are simply ignored.
Their role left undiscussed, as once you pull the thread…random with primes is what you get.
Your society is choked by money issues. Funding is more important than answers.
Turns out you don't need any general solution to binary quadratic Diophantine equations.
You can figure it out just from using x^2 - 1 = Dy^2, by noting how D must divide through x+1 and x-1.
The sad story here is I think the answer is about random.
Mathematicians avoid random with prime numbers because random can answer questions supposedly of research interest, like the Twin Primes conjecture and Goldbach's conjecture. (First: True. Second: False.)
THAT to me is the best explanation.
The behavior of primes with Pell's Equation is random, and there is no way to hide that fact with the usual obfuscations used with prime numbers, so the equations I've been so excited about, are simply ignored.
Their role left undiscussed, as once you pull the thread…random with primes is what you get.
Your society is choked by money issues. Funding is more important than answers.
# posted by James Harris @ 00:36 
