Cubes which are Sum of Five Cubes
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Theorem
The following cube numbers can be expressed as the sum of $5$ positive cube numbers:
- $9^3, \ldots$
This article is complete as far as it goes, but it could do with expansion. In particular: More terms needed. It seems that: $4$ and all numbers $> 8$ can be so expressed only $4, 8, 10, 11, 13$ require repeated cubes You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Expand}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Proof
\(\ds 9^3\) | \(=\) | \(\ds 729\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1 + 27 + 64 + 125 + 512\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1^3 + 3^3 + 4^3 + 5^3 + 8^3\) |
This article is complete as far as it goes, but it could do with expansion. In particular: Add the proof based on $9^3 = 1^3 + 6^3 + 8^3$ and $6^3 = 3^3 + 4^3 + 5^3$ from Cubes which are Sum of Three Cubes You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Expand}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $729$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $729$