Squares which are Difference between Two Cubes
Jump to navigation
Jump to search
Theorem
$169$ is the smallest square number which is the difference between two cubes:
- $169 = 8^3 - 7^3$
This article is complete as far as it goes, but it could do with expansion. In particular: Add the rest of the sequence, having found out what they are. 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
\(\ds 8^3 - 7^3\) | \(=\) | \(\ds 512 - 343\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 169\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13^2\) |
This theorem requires a proof. In particular: Establish that this is the smallest such. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. 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 {{ProofWanted}} 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
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $169$