Fibonacci numbers | Is F(m*n -1) – (F(n-1))^m always divisible by (F(n))^2 ?

 
 

Is   ( \,F_{mn - 1} \,) \; - \; ( \,F_{n-1} \,)^m    always divisible by    ( \,F_n \,)^2  

    for all   m \geq 1   and   n \geq 1

 

any counterexample?
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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