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

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Helmut Richter

Posts: 164
Registered: 7/4/06
Re: Pell type equations
Posted: Apr 27, 2012 7:57 AM
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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).

Helmut Richter

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