Fibonacci numbers – Identity

 

Establish the identity:
 

F_{14 \,r} \, (F^7_{n+4 \,r} \; + \; F^7_{n}) \; - \; 7 \, F_{10 \,r} \,(F^6_{n+4 \,r} \, F_{n} \; + \; F_{n+4 \,r} \, F^6_{n})

+ \; 21 \, F_{6 \,r} \, (F^5_{n+4 \,r} \, F^2_{n} \; + \; F^2_{n+4 \,r} \, F^5_{n})

- \; 35 \, F_{2 \,r} \, (F^4_{n+4 \,r} \, F^3_{n} \; + \; F^3_{n+4 \,r} \, F^4_{n})

= \; F^7_{4 \,r} \, F_{7n+14}

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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