Make {x^2 + 2xy + y^2, x^2 + 3xz + z^2, y^2 – 5yz + z^2} squares … Part 1

 
 
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

where   x, y, z   are positive integers.

 
Here are the first few solutions:
 

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

\{112, \; 231, \; 48, \; 343, \; 176, \; 15 \}
\{240, \; 1335, \; 176, \; 1575, \; 464, \; 799 \}
\{264, \; 744, \; 143, \; 1008, \; 451, \; 205 \}
\{456, \; 552, \; 95, \; 1008, \; 589, \; 227 \}

 
Find the next few solutions.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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