Fibonacci numbers – gcd (Part 1)

 
 
Find all ordered pairs   (m, \; n)   of positive integers for which there’s an integer   x   satisfying the equation:

gcd \,(F_m, \, F_n) \, x^2 \; - \; (F_m + F_n) \, x \; + \; F_{gcd \,(m, \,n)} \; = \; 0

 
 
Next blog:   The gcd of any two Fibonacci numbers is also a Fibonacci number
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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