Cubic Fibonacci Numbers

Theorem

The only Fibonacci numbers which are also cubes are:

$F_1 = 1 = 1^3$
$F_6 = 8 = 2^3 = 3 + 5$


Proof


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Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $8$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $8$
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