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Topic: Diophantine equation x^2-19y=8 no solution Proof!
Replies: 12   Last Post: Feb 6, 2014 9:08 AM

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Daniel Joyce

Posts: 192
Registered: 1/5/14
Re: Diophantine equation x^2-19y=8 no solution Proof!
Posted: Feb 5, 2014 7:18 PM
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On Wednesday, February 5, 2014 6:51:04 PM UTC-5, Hlauk wrote:
> On Wednesday, February 5, 2014 5:40:38 PM UTC-5, jtjim...@gmail.com wrote:
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> > Em quarta-feira, 5 de fevereiro de 2014 12h33min18s UTC-2, jtjim...@gmail.com escreveu:
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> > > This equation has no solution?
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> >
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> > >
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> > > Proof?
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> > Port563,
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> > Ok, I understood.
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> > I suppose that probability of these remainders are equally likely = 1/10.
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> > Dan,
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> > Looking at A038873 it seems to me that is for x^2 - py = 2
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> At it's header of a038873 ---
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> Primes p such that 2 is a square mod p; or, primes
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> congruent to {1, 2, 7} mod 8.
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> So in the case of prime 2 ---- x=4 and y=4 satisfying the equation.
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> 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^2-11y = 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




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