Fibonacci Num3ers | x^2 + y^2 + x = 3*x*y

 
 
Prove that if a pair of positive integers   (x, \; y)   satisfies the equation

x^2 \; + \; y^2 \; + \; x \; = \; 3 \, x \, y

then

x \; = \; ( \,F_{2n+1} \,)^2
y \; = \; ( \,F_{2n} \,)^2 \; + \; 1        or        y \; = \; ( \,F_{2 \,n+2} \,)^2 \; + \; 1

 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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