Pythagorean triangle – area

 

The integers:

a \; = \; u^2 \; - \; v^2
b \; = \; 2 \, u \, v
c \; = \; u^2 \; + \; v^2

form a Pythagorean triple.

where   u, \; v   are integers with   u \; > \; v \; > \; 0

a, \; b, \; c   are the lengths of the sides of a right triangle.

 

Prove that the area of such a triangle is not a perfect square when

u = F_{n+1} ,     v = F_{n} ,   and   n \; \geq \; 2

F_{n}   is the n-th Fibonacci number

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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