20050411, 10:31  #1 
Nov 2004
3^{2} Posts 
Looking for solutions to w^2n*x^2=z^2
How can i find solutions (w, x, z) to the following equation:
w^2n*x^2=z^2 Can i use the continued fraction expansion? and how? Is the solution related to the factorization of n? 
20050411, 11:37  #2  
Nov 2003
2^{2}×5×373 Posts 
Quote:
a change of variables) For z = 1, solution methods are well known. This is Pell's equation. For z > 1, there are extensions of the cfrac method. See Henri Cohen's book. I don't have it handy, so can't look up the exact reference. 

20050411, 18:46  #3 
Nov 2004
9_{16} Posts 
No, Henri Cohen's books do not deal with it  "A course in computacional algebraic number theory" and "Advanced topics in computacional number theory". I could only find the solution to x^2+dy^2=p with d>0 and p prime (Cornachia). I am not sure if this could be used to solve w^2n*x^2=z^2 by transforming it to z^2+n*x^2=w^2. Anyway there sould be a suitable continued fraction aproximation too but i can not find it.

20050411, 19:25  #4 
Jun 2003
1582_{10} Posts 
an easier method
w^2n*x^2=z^2 then w^2z^2=n*x^2 or (wz)* (w+z) =n*x^2 factorize n*x^2 to get solutions of w and z. Citrix 
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