Pythagorean triangle {a+b+c, a^2+b+c, a+(b+c)^2} are to made squares

 
 
Find a Pythagorean triangle   (a, \; b, \; c)   such that
 
a \; + \; b \; + \; c
a^2 \; + \; b \; + \; c
b^2 \; + \; c \; + \; a
c^2 \; + \; a \; + \; b
a \; + \; (b+c)^2
b \; + \; (c+a)^2
c \; + \; (a+b)^2
 
are all squares

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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