Timeline for Parametric solutions of Pell's equation

5 events

when toggle format	what		by	license	comment
Jan 27, 2015 at 10:20	comment	added	Stefan Kohl♦		Nobody said degree $6$ would be 'necessary' -- there are just series where degree $6$ occurs. For example, as you correctly noticed, $n = 29$ and $n = 53$ not only belong to the series with $D = 4x^2+4x+5$, where the solution with $P$ of degree $6$ stems from $\sqrt{D} = [2x+1,\overline{x,1,1,x,4x+2}]$ (odd period length, three $x$-es occur -- thus $P$ has degree $2 \cdot 3 = 6$), but also to the series with the two $D$ you mention and $\sqrt{D} = [13x-8,\overline{2,1,1,2,26x-16}]$ and $\sqrt{D} = [25x-18,\overline{3,1,1,3,50x-36}]$, respectively.
Jan 27, 2015 at 7:51	history	edited	Will Jagy	CC BY-SA 3.0	added 231 characters in body
Jan 27, 2015 at 5:47	history	edited	Will Jagy	CC BY-SA 3.0	added 143 characters in body
Jan 27, 2015 at 5:41	history	edited	Will Jagy	CC BY-SA 3.0	added 143 characters in body
Jan 27, 2015 at 5:15	history	answered	Will Jagy	CC BY-SA 3.0