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Math Forum » Discussions » sci.math.* » sci.math.independent

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 28, 2012 6:03 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Hi Helmut

"Helmut Richter" <hhr-m@web.de> wrote in message
news:alpine.LNX.2.00.1204280933150.5441@badwlrz-clhri01.ws.lrz.de...

> Whenever you see a Diophantine equation of the form
>
> ax² + by² + c = 0
>
> you should, before thinking, see what happens if taken modulo m for each m
> which is:
>
> - the number 8
>

I think I understand the following two, but why the number 8 ?

Thanks again,

Terry

> - p² for a prime p>2 if p² ist a factor of a, b, or c or if p is a
> factor of more than one of these
>
> - a prime p>2 that is a simple factor of one of a, b, or c
>
> Often, the complexity reduces or it can be shown that there are no
> solutions.
>
> --
> Helmut Richter




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