Fibonacci Number equal to Sum of Sequence of Cubes
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Theorem
The following Fibonacci number can be expressed as the sum of a sequence of cubes:
- $F_{18} = 2584 = 7^3 + 8^3 + 9^3 + 10^3$
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Proof
\(\ds 2584\) | \(=\) | \(\ds 343 + 512 + 729 + 1000\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 7^3 + 8^3 + 9^3 + 10^3\) |
$\blacksquare$
Historical Note
In his Curious and Interesting Numbers, 2nd ed. of $1997$, David Wells attributes this result to Michal Stajsczak, but gives no context.
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2584$