{x+y, x+z, y+z} are all squares, and 2(x+y+z) a biquadrate

 
 
Find three positive integers   x, \; y, \; z   the sum of any two of which is a square:

x \; + \; y \; = \; a^2
x \; + \; z \; = \; b^2
y \; + \; z \; = \; c^2

and double the sum of all three is a biquadrate:

2 \,(x + y + z) \; = \; d^4

 

 
 

 
 

 
 

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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