20201006, 13:18  #1 
Jul 2014
3·149 Posts 
finding unimodular substitutions
Hi,
does anyone know a method for finding a unimodular substitution from one binary quadratic form ( \( ax^2 + bxy + cy^2 \) ) to another given that they are equivalent? I'd like a find a unimodal substitution \(x\prime = \alpha x + \beta y \) \(y\prime = \gamma x + \delta y \) with integer coefficients which transforms \(29x^2 + 256xy + 565y^2\) into \(x^2 + y^2 \) Can anyone help? Last fiddled with by wildrabbitt on 20201006 at 13:24 Reason: latex wasn't coming out right 
20201010, 04:54  #2 
"William"
May 2003
New Haven
23×103 Posts 
x' = 5 x + 22 y
y' = 2 x + 9 y Start with the "obvious" 29 = 5^{2} + 2^{2} 
20201010, 16:54  #3 
Jul 2014
110111111_{2} Posts 
Thanks.

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