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

 
 

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 \}

\{ 112, \; 259, \; 48, \; 147, \; 176, \; 85 \}
\{ 456, \; 888, \; 95, \; 432, \; 589, \; 613 \}
\{ 1488, \; 3216, \; 527, \; 1728, \; 2201, \; 1465 \}
\{ 4720, \; 9520, \; 1239, \; 4800, \; 6431, \; 5761 \}
\{ 11088, \; 22995, \; 3344, \; 11907, \; 15664, \; 12469 \}
\{ 23352, \; 44520, \; 4031, \; 21168, \; 29051, \; 33181 \}
\{ 30096, \; 59499, \; 6992, \; 29403, \; 39824, \; 38845 \}
\{ 42784, \; 80416, \; 6303, \; 37632, \; 51761, \; 63025 \}
\{ 66352, \; 127699, \; 12528, \; 61347, \; 83984, \; 92005 \}
\{ 127920, \; 241995, \; 20336, \; 114075, \; 156784, \; 185389 \}

 
 

Find the next few solutions.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

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