Hardy-Ramanujan Number/Examples/6,963,472,309,248
Jump to navigation
Jump to search
Theorem
The $4$th Hardy-Ramanujan number $\operatorname {Ta} \left({4}\right)$ is $6 \, 963 \, 472 \, 309 \, 248$:
\(\ds 6 \, 963 \, 472 \, 309 \, 248\) | \(=\) | \(\ds 2421^3 + 19 \, 083^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 5436^3 + 18 \, 948^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 10 \, 200^3 + 18 \, 072^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13 \, 322^3 + 16 \, 630^3\) |
Historical Note
It is widely reported that the $4$th Hardy-Ramanujan number $\map {\operatorname {Ta} } 4$ was discovered by E. Rosenstiel, J.A. Dardis and C.R. Rosenstiel in $1991$.
However, David Wells reports in his Curious and Interesting Numbers, 2nd ed. of $1997$ that this result can be found in the Numbers Count column of Personal Computer World, November $1989$.
Proof
This theorem requires a proof. 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
- July 1991: E. Rosenstiel, J.A. Dardis and C.R. Rosenstiel: The Four Least Solutions in Distinct Positive Integers of the Diophantine Equation $s = x^3 + y^3 = z^3 + w^3 = u^3 + v^3 = m^3 + n^3$ (The Institute of Mathematics and its Applications Bulletin Vol. 27: pp. 155 – 157)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6,963,472,309,248$