Pythagorean triangles {a^2 + b^2 ± a*b/2, a^2 + b^2 ± a*b} to be made squares

 
 
Solve

(1)

(a^2 + b^2) \; - \; a \, b \; = \; n^2
(a^2 + b^2) \; + \; a \, b \; = \; m^2

(2)

(a^2 + b^2) \; - \; 1/2 \, \cdot \, a \, b \; = \; p^2
(a^2 + b^2) \; + \; 1/2 \, \cdot \, a \, b \; = \; q^2

 

where   (a, \; b)   are the two odd legs in a Pythagorean triangle.

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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