Hardy-Ramanujan Number/Examples/48,988,659,276,962,496

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Theorem

The $5$th Hardy-Ramanujan number $\operatorname {Ta} \left({5}\right)$ is $48 \, 988 \, 659 \, 276 \, 962 \, 496$:

\(\displaystyle 48 \, 988 \, 659 \, 276 \, 962 \, 496\) \(=\) \(\displaystyle 38 \, 787^3 + 365 \, 757^3\)
\(\displaystyle \) \(=\) \(\displaystyle 107 \, 839^3 + 362 \, 753^3\)
\(\displaystyle \) \(=\) \(\displaystyle 205 \, 292^3 + 342 \, 952^3\)
\(\displaystyle \) \(=\) \(\displaystyle 221 \, 424^3 + 336 \, 588^3\)
\(\displaystyle \) \(=\) \(\displaystyle 231 \, 518^3 + 331 \, 954^3\)


Proof


Historical Note

In his Curious and Interesting Numbers, 2nd ed. of $1997$, David Wells attributes this to J.A. Dardis, in the Numbers Count column of Personal Computer World, February $1995$.


Sources