
Re: Diophantine equation x^219y=8 no solution Proof!
Posted:
Feb 5, 2014 7:18 PM


On Wednesday, February 5, 2014 6:51:04 PM UTC5, Hlauk wrote: > On Wednesday, February 5, 2014 5:40:38 PM UTC5, jtjim...@gmail.com wrote: > > > Em quartafeira, 5 de fevereiro de 2014 12h33min18s UTC2, jtjim...@gmail.com escreveu: > > > > > > > This equation has no solution? > > > > > > > > > > > > > > Proof? > > > > > > > > > > > > Port563, > > > > > > Ok, I understood. > > > > > > I suppose that probability of these remainders are equally likely = 1/10. > > > > > > > > > > > > Dan, > > > > > > Looking at A038873 it seems to me that is for x^2  py = 2 > > At it's header of a038873  > > > > Primes p such that 2 is a square mod p; or, primes > > congruent to {1, 2, 7} mod 8. > > > > So in the case of prime 2  x=4 and y=4 satisfying the equation. > > > > Dan
Hi Port563,
For this particular equation it is relevant to this sequence a038873. because primes congruent to {1, 2, 7} mod 8. where (8) is the key.
I tried this with prime 11  x^211y = 8 and starting with 5^2 8 the residual pattern was more complex then 19, mainly  6,8,7,3,7,8,6,1,4,4,1,6,1 then repeats the pattern  6,8,7,3,7,8,3,1,4,4,1,6,1 ..
Cheers,
Dan

