Thursday, April 19, 2007
JSH: Hard success
I started with
2975x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)
and stepped through a straightforward bit of algebra where I say I relied on the principle that
p(a+b)*(c+d) = (p*a + p*b)*(c+d)
without regard to the value of 'a' and 'c' but I think some of you think, wait a minute, what if 'a' and 'c' are algebraic numbers—as I haven't mentioned a ring—and they divide off factors in common with p?
I have various proofs that address that issue but none of them have resonated so I figured out another which was different from what I thought would work, where I've said that before these last couple of days, and been wrong.
The problem with my previous approach yesterday was that I figured out an angle that forced a function I call g(x) to be an integer function with integer x, given the conditions I was using, which I realized today didn't help me.
So I was stuck, again, trying to figure out some other path, some other way, hoping against hope that I wasn't actually wrong…but maybe I was?
So I finally faced reality, and noted that my argument if true with the two derivations I am now using would require that at least one solution match between two different quadratics at least to unit factors, and I came up with another way, and the answer seems so hard to explain.
It's a difference between squares of factors with 289 or 49 versus 17 and 7 and I wonder if anything can convince you people and does it really matter?
I just came up with it today and maybe tomorrow I'll find a mistake, but it's such a brilliant idea.
Succinctly, my argument required that except for unit factors, I could match ONE root of two different quadratics to each other—if I was right.
Pursuing that path I found that I appear to have a direct proof that I am right—if I didn't make some stupid mistake.
But that proof requires that you understand the difference between squares of factors, in this case, squares of factors of 289 or 49, versus factors of 17 and 7.
Such an odd thing and what does it really mean?
What if I DID make a mistake, yet again? What if I just screwed up, one more time?
But I didn't.
I don't know where that answer came from, and that kind of scares me. How did I ever figure out to take that path?
Mu.
2975x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)
and stepped through a straightforward bit of algebra where I say I relied on the principle that
p(a+b)*(c+d) = (p*a + p*b)*(c+d)
without regard to the value of 'a' and 'c' but I think some of you think, wait a minute, what if 'a' and 'c' are algebraic numbers—as I haven't mentioned a ring—and they divide off factors in common with p?
I have various proofs that address that issue but none of them have resonated so I figured out another which was different from what I thought would work, where I've said that before these last couple of days, and been wrong.
The problem with my previous approach yesterday was that I figured out an angle that forced a function I call g(x) to be an integer function with integer x, given the conditions I was using, which I realized today didn't help me.
So I was stuck, again, trying to figure out some other path, some other way, hoping against hope that I wasn't actually wrong…but maybe I was?
So I finally faced reality, and noted that my argument if true with the two derivations I am now using would require that at least one solution match between two different quadratics at least to unit factors, and I came up with another way, and the answer seems so hard to explain.
It's a difference between squares of factors with 289 or 49 versus 17 and 7 and I wonder if anything can convince you people and does it really matter?
I just came up with it today and maybe tomorrow I'll find a mistake, but it's such a brilliant idea.
Succinctly, my argument required that except for unit factors, I could match ONE root of two different quadratics to each other—if I was right.
Pursuing that path I found that I appear to have a direct proof that I am right—if I didn't make some stupid mistake.
But that proof requires that you understand the difference between squares of factors, in this case, squares of factors of 289 or 49, versus factors of 17 and 7.
Such an odd thing and what does it really mean?
What if I DID make a mistake, yet again? What if I just screwed up, one more time?
But I didn't.
I don't know where that answer came from, and that kind of scares me. How did I ever figure out to take that path?
Mu.
# posted by James Harris @ 01:32 
