Re: Computability

On Jan 13, 7:34 pm, The Dougster 22044 <DGo...@xxxxxxxxxxxx> wrote:
On Jan 10, 11:16 am, quasi <qu...@xxxxxxxx> wrote:

You claimed to have checked it up to z = 256, but apparently you
missed the following counterexample:

  (x,y,z) = (74,129,143) which has signature (6,3,3).

Thanks to quasi for the smallest triple with the right prime
signature. Well done!

(74, 129, 143) Really, that is good work. To limit = 143, my program
checked 1,415 triples coprime and with the inequality, from 343,000
generated triples. Wow.

P.P.S. I think another condition is x + y == z mod p. I am working to
understand that one....

Two things here: We have x^p + y^p = z^p or z | x^p + y^p, and then we
have in my P.P.S. that x+y = z mod p. Where did I get that? Well, in
AA we learned that for prime modulus p, x^p + y^p = (x+y)^p mod p, The
Student's Equality. (Students in algebra frequenetly write this in a
non-modular form; that is a mistake.) So:

x^p + y^p = z^p
(x + y)^p == z^p mod p
(x + y)^p - z^p == 0 mod p
(x + y - z)^p == 0 mod p
x + y - z == 0 mod p or
p | x + y - z

Agreed?

Doug
x
.

Relevant Pages

  • Re: Computability
    ... probablilities, too. ... it has the signature, it doesn't pass that one test: ... checked 1,415 triples coprime and with the inequality, from 343,000 ... The smallest triple with the inequality and the coprimality is ...
    (sci.math)
  • Re: Computability
    ... missed the following counterexample: ... signature. ... checked 1,415 triples coprime and with the inequality, from 343,000 ...
    (sci.math)
  • Re: Computability
    ... missed the following counterexample: ... signature. ... checked 1,415 triples coprime and with the inequality, from 343,000 ...
    (sci.math)