
Re: Pell type equations
Posted:
Apr 27, 2012 7:57 AM


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

