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 2020-10-06, 13:18 #1 wildrabbitt   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 2020-10-06 at 13:24 Reason: latex wasn't coming out right
 2020-10-10, 04:54 #2 wblipp     "William" May 2003 New Haven 23×103 Posts x' = 5 x + 22 y y' = 2 x + 9 y Start with the "obvious" 29 = 52 + 22
 2020-10-10, 16:54 #3 wildrabbitt   Jul 2014 1101111112 Posts Thanks.

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