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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 27, 2012 8:51 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Hi

"Helmut Richter" <hhr-m@web.de> wrote in message
news:alpine.LNX.2.00.1204271351050.14648@badwlrz-clhri01.ws.lrz.de...
> On Fri, 27 Apr 2012, Terry M wrote:
>
>> where x and y are coprime but can find no such solutions for 5x^2 + 45 =
>> y^2
>
> Without the restriction of coprimeness there are solutions, e.g. x=6, y=15
>
> With this restriction, there are none:
>
> A square is 0, 1, 4, or 7 (mod 9)
> Five times a square os 0, 5, 2, or 8 (mod 9)
>
> So the equation can only be fulfilled when both 5x^2 and y^2 are 0 (mod
> 9).
>

So I was making hard work of it, lol

Many thanks Helmut ;-)


> --
> Helmut Richter




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