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Age 16 to 18
Challenge Level 
Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
This problem complements the material in the article The Golden Ratio, Fibonacci Numbers and Continued Fractions.
For a sequence of, mainly more elementary, problems on these topics see Golden Mathematics.
For a sequence of, mainly more elementary, problems on these topics see Golden Mathematics.
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Fibonacci Factors
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