Make {x^2 – 2xy + y^2, x^2 – 3xz + z^2, y^2 + 5yz + z^2} squares … Part 3

 
 
Find three positive integers   x, y, z   such that   (x, y, z) = 1   and

x^2 \; - \; 2 \,x \,y \; + \; y^2 \; = \; A^2
x^2 \; - \; 3 \,x \,z \; + \; z^2 \; = \; B^2
y^2 \; + \; 5 \,y \,z \; + \; z^2 \; = \; C^2

 
Here are the first few solutions
 

\{ \, x, \; y, \; z, \; A, \; B, \; C \, \}

\{ \, 8, \; 15, \; 24, \; 7, \; 8, \; 51 \, \}
\{ \, 60, \; 123, \; 160, \; 63, \; 20, \; 373 \, \}
\{ \, 104, \; 216, \; 273, \; 112, \; 13, \; 645 \, \}

 
find the next few solutions
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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