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Topic: Pell type equations
Replies: 29   Last Post: Apr 29, 2012 5:37 PM

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Terry M

Posts: 15
Registered: 4/26/12
Re: Pell type equations
Posted: Apr 29, 2012 9:36 AM
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"Helmut Richter" <hhr-m@web.de> wrote in message
news:alpine.LNX.2.00.1204291311200.5595@badwlrz-clhri01.ws.lrz.de...
> On Sun, 29 Apr 2012, Terry M wrote:
>

>> correction: so 3x² + 7y² is never 1, 5 or 6 (Mod 8)
>
> This is 100% correct.
>
> I mentioned only the 6 as example but the others are correct as well.
> The 1 and 5 could have been caught modulo 4, but for the 6 it is necessary
> to check modulo 8.
>


ok.

The equation I am working on is (a^2 + b^2)(c^2 + d^2) = x^2
with d > c >= b > a > 0, a and b are coprime, c and d are coprime
and I am aware of the Brahmagupta-Fibonacci identity.

If a and b are known, what (if anything) can be deduced about c and d.

My original examples were where a=1, b=2 and c=2 and 3 respectively
It has now been shown that where c=2 there are many (infinite) values for d
and where c=3 there are no possible values for d within the constraints.

> --
> Helmut Richter





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